Math II Name_____________________ Pd ____HW Packet

Unit 5: Probability

Day Lesson Homework Stamp

Day 1 Basic Probability

Day 2 Basic Probability

Day 3 Independent/Dependent Events

Day 4 Independent/Dependent Events

Day 5 Practice Day & QUIZ

Day 6 Exclusive/Inclusive Events

Day 7 Exclusive/Inclusive Events

Day 8 Practice Day & QUIZ

Day 9 Conditional Probability

Day 10 Conditional Probability

Day 11 Review

Day 12 Test #7: Probability

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Foundations of Math 2 – Unit 7: ProbabilityDay 1 – Basic Probability

1. Consider the following scenario.Jessica rolls a 6-sided die. What are all the possible outcomes?

2. Consider the following scenario.Harley flips a coin. What are the possible outcomes?

3. Now what if Harley were to flip a second coin, so two total coins are flipped. a) Does the sample space of the first coin change?

b) Now consider the following tree diagram.When Harley flips the first coin, the 2 options are H or T.From there, he could either flip H or T on the second flip.

HH

TH

TT

c) Draw a tree diagram showing the possibilities if Harley flips 3 coins.

d) List the sample space of all the possible outcomes when he flips 3 coins. Make sure you use brackets.

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Basic Probability:The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes.

We notate this as P (event )= FavorableOutcomesTotalnumber of possible outcomes

4. Recall the sample space of rolling a 6-sided die. Rewrite it here.

Now find the following probabilities.P (2 ) This means the probability of rolling a 2.

P(3 or 6) (Probability of rolling a 3 or a 6)

You try!P(odd) (Probability of rolling an odd number)

P(not a 4) (Probability of rolling anything but a 4)

P(1,2,3,4,5, or 6) (Probability of rolling any of the possible numbers)

P(8) (Probability of rolling an 8)

5. Relist the sample space for tossing two coins:

Find the following probabilities:P(two heads) P(one head and one tail) P(head, then tail)

P(all tails) P(no tails)

6. Two 6-sided dice are rolled. In the following table, record the sums of the two rolls. This table represents every possible outcome.

Find the following probabilities:P(a 1 and a 4) P(a 1, then a 4) P(sum of 8)

P(sum of 12) P(doubles) P(sum of 15)

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Intersection of two sets (A B): The set of all elements in both sets A and B.

Union of two sets (A B): The set of all elements in set A or set B.

Example: Given the following sets, find A B and A BA = {1,3,5,7,9,11,13,15} B = {0,3,6,9,12,15}

A B: (everything in A and B)A B=

A B: (everything in A or B. Do not repeat values used more than once).A B=

7. An experiment consists of tossing three coins. a) List the sample space for the outcomes of the experiment.

b) Find the following probabilities:

P(all heads) _________________

P(two tails) _________________

P(no heads) _________________

P(at least one tail) _____________

8. A bag contains six red marbles, four blue marbles, two yellow marbles and 3 white marbles. One marble is drawn at random.a) What is the sample space for this experiment? b) Find the following probabilities:

P(red) ____________

P(blue or white) ____________

P(not yellow) ____________

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1. Suppose a box contains three balls: one red, one blue, and one white. One ball is selected, its color is observed, and then the ball is placed back in the box. The balls are scrambled, and again, a ball is selected and its color is observed. What is the sample space of the experiment?

2. Suppose you have a jar of candies: 4 red, 5 purple and 7 green. Find the following probabilities of the following events:

A) Selecting a red candy.

B) Selecting a purple candy.

C) Selecting a green or red candy.

D) Selecting a yellow candy.

E) Selecting any color except a green candy.

3. A)What is the sample space for a single spin of a spinner with red, blue, yellow and green sections spinner?

B) If the spinner is equally likely to land on each color, what is the probability of landing on red in one spin?

C) What is the sample space for 2 spins of the first spinner?

D) What is the probability of landing on green both times in two spins?

4) Given the following sets,

A: {2,4,6} B: {1,2,3}find A B and A B.

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5.

6.

7.

8.

7 & 8.

Day 1 classwork Name_________________________

1. A number is chosen at random from 1 to 50. Find the probability of selecting an odd number.

2. A number is chosen at random from 1 to 50. Find the probability of selecting a multiple of 10.

3. A number is chosen at random from 1 to 25. Find the probability of selecting an even number that is greater than 13.

For #4-6, refer to the table in your notes.4. Jerry rolls two 6-sided dice. Find the probability of him rolling a 5 or greater on the first die, and a 4 or greater on the second die.

5. What is the total number of possible outcomes when rolling a pair of dice?

6. Find the probability of rolling an odd number on the second die.

Use the following spinner for #7-13.7. What is the probability of the spinner landing on a 1 or 3?

8. What is the probability of the spinner landing on 2 or 4?

9. What is the probability of the spinner not landing on 2 or 4?

10. What is the probability of the spinner not landing on 3?

11. What is the probability of the spinner landing on 4?

12. Do you have an equal chance of landing on either a 2 or 4?

13. Do you have an equal chance of landing on either a 1 or 2?

14. List the sample space for flipping four coins.

15. Using that sample space, find the probability of flipping exactly 3 heads.

16. What is the probability of flipping at least 2 tails?

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Foundations of Math 2 – Unit 7: ProbabilityDay 2 – Basic Probability

Warm-Up

1. What is the probability of landing on tails when you toss one coin?

2. What is the probability of rolling a 2 or 3 on a six-sided number cube?

3. What is the probability of spinning a number greater than 2 on a six sectioned spinner numbered 1-6?

4. (3 xy )2 5.3 x2 y5

6 y8 x−1 6. (5 x3 z )0 7. ( x−1 x3y5 )

−2

8. 9

3x2 y−2

8

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_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

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_____________

_______________________________________________

_______________________________________________

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Foundations of Math 2 – Unit 7: ProbabilityDay 3 – Independent/Dependent Events

Warm-Up

1. How many outfits can you make if you have 4 shirts, 5 pairs of shorts and 3 pairs of shoes?

2. How many different combinations are there for a lock if there are 3 numbers in the combination, 0-9 and they can be repeated?

3. Find the probability of landing on a multiple of three.

4. Find the probability of landing on a number greater than 11 or a 1.

5. You spin the spinner twice. Find the probability of landing on a multiple of 6 and then an 8.

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x

x

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Foundations of Math 2 – Unit 7: ProbabilityDay 4 – Independent/Dependent Events

Warm-Up

Determine if #1-2 are independent or dependent. Explain.1. A student spins a spinner and rolls a number cube.

2. A student picks a raffle ticket from a box and then picks a second raffle ticket without replacing the first ticket.

Find the probability of the following.3. A bag contains 6 black and 4 red checkers. Find the probability of drawing a black checker, replacing it, and drawing another black checker.

4. Rolling a 6 on the first die and rolling an odd number on the second die.

5. Flipping a tail on a coin and spinning a 5 on a spinner with equal sections labeled 1-5.

6. You have nine cards labeled 1-9. Find the probability of drawing a 1,2 or 3 , replacing the card, then drawing a 7,8 or 9.

7. There are 4 black marbles and 2 white marbles in a bag. What is the probability of choosing a black marble, not replacing it, then choosing a white marble?

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1. A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green?

2. A box contains a penny, nickel, and a dime. Find the probability of choosing a dime first, and then without replacing it, choosing a penny.

3. A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on heads and rolling a 3.

4. The teacher of a class that contains 12 boys and 16 girls needs to pick 2 volunteers. She randomly selects one student, and then selects another student. Find the probability thata) she chooses a girl first, then a boy

b) she chooses 2 boys

5. A bag contains 9 black checkers and 6 red. Find the probability of drawing a red, replacing it, then drawing another red.

6. A bag contains 9 black and 6 red checkers. Find the probability of drawing a black, replacing it, then drawing a red.

7. Rolling a 1,2, or 3 on the first roll of a 6-sided die, then rolling a 4 on the second roll.

8. Randy has 4 pennies, 2 nickels and 3 dimes in his pocket. If he randomly chooses 2 coins, what is the probability that both are dimes?

Determine if #9-11 are independent or dependent. Explain9. A student spins a spinner and chooses a Scrabble tile.

10. A boy chooses a sock from a drawer of socks, then chooses a second sock without replacing the first.

11. A student picks a raffle ticket from a box, replaces the ticket, then picks a second raffle ticket.

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Day 4 Classwork Name____________________

1. Dr. Thomas has infected Captain Amazing with a combination of deadly viruses. Captain Amazing was able to find Dr. Thomas’ lab which was full of different vials and potions. There are 9 green vials, 6 purple vials, and 3 black vials.a) If there are 3 vials that could cure Captain Amazing, what is the probability that he is able to pick a vial that contains a cure?

b) Dr. Thomas has cut the power to his lab to try and thwart Captain Amazing. Since he cannot see what he is grabbing due to the darkness,

i. What is the probability that Captain Amazing grabs 1 green vial?

ii. What is the probability that Captain Amazing grabs 1 purple vial?

iii. What is the probability that Captain Amazing grabs 2 black vials?

iv. What is the probability that Captain Amazing grabs 1 green vial, then grabs 1 purple vial (w/o replacement)?

v. What is the probability that Captain Amazing grabs 1 black vial, then grabs 1 green vial, then grabs another black vial (w/o replacement)?

c) While the power was out 4 green vials and 2 purple vials were smashed. What is the probability that Captain Amazing is able to select a black vial from the remaining vials?

2. Nicholas loves his video games and has a huge collection of them. His collection has 10 Role-playing games, 15 Shooter games, and 20 Sports games. Mickey comes over to borrow a video game. Mickey picks the games at random since he doesn’t care what games he gets to play.a) What is the probability that Mickey picks a shooter game?

b) What is the probability that Mickey picks a sports game?

c) What is the probability that Mickey picks a role playing game, then picks a shooter game (w/o replacement)?

d) what is the probability that Mickey picks a sports game, then another sports game, then a third sports game (w/o replacement)?

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3. Officer Smythe is trying to defuse a bomb that was set by Dr. Thomas to destroy Hero City. After opening the bomb, officer Smythe sees 4 red wires, 6 green wires, 3 black and 2 blue wires.a) What is the probability that Officer Smythe cuts a red wire to defuse the bomb?

b) What is the probability that Officer Smythe cuts a red or a green wire to defuse the bomb?

c) What is the probability that Officer Smythe cuts a wire that is not blue to defuse the bomb?

d) What is the probability that Officer Smythe cuts a green wire, then cuts a blue wire, then a black wire?

e) What is the probability that Officer Smythe cuts a red, then a green, then another red?

4. The Grinch has been raiding Whoville stealing things that remind him of Christmas. He has 4 ornaments, 3 stockings, 2 christmas wreaths and a Christmas tree. You sneak into his dark cave to steal holiday items back from him.a) What is the probability that you steal 1 ornament?

b) What is the probability that you steal 1 wreath?

c) What is the probability that you steal 1 stocking and then 1 ornament?

d) What is the probability that you steal 2 ornaments and 1 wreath?

e) What is the probability that you do not steal the Christmas tree?

5. Dr. Thomas has used the chaos and is making Lady Justice play a deadly game. He has placed 5 red bombs and 5 black bombs in a box. In each round you have to pick bombs and then place it back into the box.a) In round one, what is the probability that Lady Justice picks a red bomb and then a black bomb?

b) In round two, what it he probability that Lady Justice picks a red and then another red?

c) In round three, what is the probability that Lady Justice picks 3 black bombs in a row?

d) In round four, what is the probability that Lady Justice picks 6 red bombs in a row?

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Foundations of Math 2 – Unit 7: ProbabilityDay 5 – Practice

Warm-Up

1. Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting a green marble from Bag A and one black marble from Bag B.

2. A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Two consecutive draws are made from the box without replacement of the first draw. Find the probability of each event.a) P(orange first, then green)

b) P( both marbles are purple)

c) P (purple first, then any color except purple)

3. Two seniors, one from each government class are randomly selected to travel to Washington DC. Wes is in a class of 18 students and Maureen is in a class of 20 students. Find the probability that both Wes and Maureen will be selected. Are these independent or dependent?

4. If there was only one government class, and Wes and Maureen were in that class of 38 students, what would be the probability that both Wes and Maureen would be selected as the two students to go to Washington? Is this an example of independent or dependent probabilities?

5. A 6-sided die is rolled and a spinner with the letters A-Z is spun.a) How many outcomes are there?

b) P(1 and A)

c) P (odd and B)

6. In a bag there are 2 red marbles, 3 white marbles and 5 blue marbles. Once a marble is selected, it is NOT replaced. Find the following probabilities.a) P (red, then white)

b) P (blue, then red)

c) P (red, red, red)

d) P (blue, blue, white)

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1. In a bag there are 2 red marbles, 3 white marbles and 5 blue marbles. Once a marble is selected, it IS replaced. Find the following probabilities.a) P (white, then blue)

b) P (white, then white)

c) P (blue, white, red)

d) P (blue, blue, blue)

2. Find the number of possible outcomes in the sample space. a) You toss 4 coins.

b) You roll a number cube and toss 2 coins.

c) You have 5 shirts, 4 pairs of paints and 6 pairs of shoes. How many outfits could you make?

3. A bag contains 12 purple marbles and 8 blue marbles. You choose a marble at random.a) What is the probability of selecting a purple marble?

b) You randomly select 2 marbles, one right after the other. What is the probability that you pick a purple marble, followed by a blue marble? The first marble was not replaced.

c) With replacement, what is the probability of pulling a purple marble, followed by another purple marble?

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4. A bucket contains 10 tennis balls labeled: A, A, B, C, C, C, C , D, E, Ea) What is the probability of pulling a ball labeled with C?

b) What is the probability of drawing a ball labeled with something other than a B?

c) Sam reaches into the bucket and pulls out two tennis balls. She pulls out an A and does not return it. What is the probability that the second tennis ball will be another A?

d) What is the probability of pulling an E, not replacing it, and then pulling a C?

e) What is the probability of pulling an A or B?

5. The manager at a Mexican Restaurant tracked a random sample of customers so that he could order correctly for the upcoming week. The table shows the results of a random sample of 60 customers’ orders. The manager knows that on average, the restaurant serves 2500 meals per week.

Type of Meal Chicken Beef Pork VeggieBurrito 11 9 6 5Bowl 3 5 1 7Salad 4 1 0 1Tacos 2 3 2 0

a) Based on the results of the sample, how many chicken burritos should the manager have ordered for the next week?

b) Based on the results of the sample, how many tacos should be ordered for next week?

c) If a customer were randomly chosen, what is the probability that that customer ordered a Beef Burrito?

d) If a customer were randomly chosen, what is the probability that that customer ordered a salad?

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Foundations of Math 2 - Unit 7: ProbabilityDay 6: Mutually Exclusive & Inclusive Probability

Warm-Up

1. A bucket contains 10 tennis balls labeled: A, A, B, C, C, C, C , D, E, E

a) What is the probability of pulling a ball labeled with D?

b) What is the probability of drawing a ball labeled with something other than a C?

c) Sam reaches into the bucket and pulls out two tennis balls. She pulls out an B and does not return it. What is the

probability that the second tennis ball will be an A?

d) What is the probability of pulling an D, not replacing it, and then pulling a B?

e) What is the probability of pulling an C or B?

2. Janis looks in her closet and has 76 pairs of shoes. If 16 pairs are damaged in some way, find the probability of her randomly picking an undamaged pair of shoes.

3. Is #2 based on theoretical or experimental probability?

4. What are the ODDS in favor of picking an undamaged pair of shoes?

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Mutually Exclusive - when two events ________________ happen at the same time.**You will _____________ have any outcomes in common.

Examples of mutually exclusive events:- Turning left and turning right- Tossing 1 coin and getting heads and tails- In cards: drawing 1 card and getting a king and an ace

Mutually Inclusive - when two events ____________ happen at the same time.** You will have outcomes in ________________.

Examples of mutually inclusive events:-Turning your head left and scratching your head-In cards: kings and hearts

For both exclusive and inclusive events, we will use the formula: ____________________________________________** For exclusive events, P(A and B) = 0** For inclusive events, P (A and B) ¹ 0

Example #1:A card is drawn randomly from nine cards labeled 1 through 9. a) What is the probability of picking a 5 or an even number? Are these events exclusive or inclusive?

b) What is the probability of picking a number less than 4 or a 2? Are these events exclusive or inclusive?

c) What is the probability of picking an odd number or a number less than 3? Are these events exclusive or inclusive?

d) What is the probability of picking a 1 or a number greater than or equal to 7? Are these events exclusive or inclusive?

e) What is the probability of picking a 3 or a number greater than 9? Are these events exclusive or inclusive?

f) What is the probability of picking a 2 or an even number? Are these events exclusive or inclusive?

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2. Suppose you are rolling a six-sided die. a) What is the probability that you roll an odd number or a 2? Are these events exclusive or inclusive?

b) What is the probability that you roll an odd number or a number less than 4? Are these events exclusive or inclusive?

3. If you randomly choose one of the integers from 1-10, what is the probability of choosing either an odd number or an even number? Are these events exclusive or inclusive?

4. Two 6 sided die are rolled. What is the probability of getting a sum less than 7 or a sum equal to 10? Hint: make a table. Are these events exclusive or inclusive?

5. A bag contains 26 tiles with a letter on each, one for each letter of the alphabet. What is the probability of reaching into the bag and randomly choosing a tile with one of the first 10 letters of the alphabet on it or randomly choosing a tile with a vowel on it (A, E, I, O, U)?

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1. Thomas bought a bag of jelly beans that contained 10 red jelly beans, 15 blue jelly beans, and 12 green jelly beans. What is the probability of Thomas reaching into the bag and pulling out a blue or green jelly bean?

2. 3 coins are tossed simultaneously. What is the probability of getting 3 heads or 3 tails? Are these events mutually exclusive?

3. In question 2, what is the probability of getting 3 heads and 3 tails when tossing the 3 coins simultaneously?

4. Suppose 2 events are mutually exclusive events. If one of the events is randomly choosing a boy from the freshman class of a high school, what could the other event be? Explain your answer.

5. Jack is a student in Bluenose High School. He noticed that a lot of the students in his math class were also in his chemistry class. In fact, of the 60 students in his grade, 28 students were in his math class, 32 students were in his chemistry class, and 15 students were in both his math class and his chemistry class. He decided to calculate what the probability was of selecting a student at random who was either in his math class or his chemistry class, but not both. Draw a Venn diagram and help Jack with his calculation.

6. A bag contains 26 tiles with a letter on each, one tile for each letter of the alphabet. What is the probability of reaching into the bag and randomly choosing a tile with one of the letters in the word ENGLISH on it or randomly choosing a tile with a vowel on it?

7. Are randomly choosing a teacher and randomly choosing a father mutually inclusive events? Explain your answer.

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Day 6 Classwork Name___________________________For questions 1-12, determine whether the events are mutually exclusive. Then, find each probability.1. There are 3 literature books, 4 algebra books, and 2 biology books on a shelf. If a book is randomly selected, what is the probability of selecting a literature book or an algebra book?

2. A die is rolled. What is the probability of rolling a 5 or a number greater than 3?

3. In the Math Club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the Math Club at a statewide math contest?

4. One tile with each letter of the alphabet is placed in a bag, and one is drawn at random. What is the probability of selecting a vowel or a letter from the word equation?

5. Each of the numbers from 1 to 30 is written on a card and placed in a bag. If one card is drawn at random, what is the probability that the number is a multiple of 2 or a multiple of 3?

6. Keisha has a stack of 8 baseball cards, 5 basketball cards, and 6 soccer cards. If she selects a card at random from the stack, what is the probability that it is a baseball or a soccer card?

7. There are 8 girls and 8 boys on the student senate. Three of the students are seniors. What is the probability that a person selected from the student senate is not a senior?

8. A die is rolled. What is the probability of rolling a 2 or a 6?

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Foundations of Math 2 – Unit 7: ProbabilityDay 7 – Exclusive/Inclusive Events

Warm-Up

1. Cassidy is looking for someone to take her to Homecoming this year. She has been asked by 3 freshmen, 5 sophomores, 10 juniors, and 22 seniors. What is the probability that she will choose to go with a sophomore or a junior?

2. The Football Championship can only be won by one team. There are 3 teams from the south, 4 teams from the Midwest, 2 teams from the west and 1 team from the east who could win the title. What is the probability that the National Champion will be either from the Midwest or the West?

3. The following is a set of data for a school about the favorite sports:Football Basketball Total

North Carolina 140 320 460Duke 80 260 340Total 220 580 800

a) How many people like Carolina?_______ What is the probability that someone surveyed likes Carolina?_____

b) How many people like basketball? ________ What is the probability that someone surveyed likes basketball?______

c) How many people like both Carolina and basketball? _____________

d) What is the probability that someone surveyed likes Carolina or basketball?

4. A bag contains 26 tiles with a letter on each, one tile for each letter of the alphabet. What is the probability of reaching into the bag and randomly choosing a tile with one of the last 5 letters of the alphabet on it or randomly choosing a tile with a vowel on it?

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Probability Practice:Basic Probability, Mutually Exclusive vs. Inclusive, Independent and Dependent EventsWhen you are finding probabilities:

If you want to find the probability of exactly one thing occurring, use basic probability formula:

If you want to find the probability of one OR another thing occurring, use either mutually exclusive or inclusive formulas:

If you want to find the probability of two or more events occurring (AND), use the independent or dependent formulas:

o When a problem says “with replacement”, that means that whatever was taken out was replaced before the probability of the next event is calculated. This is INDEPENDENT.

o When the problem says “without replacement”, that means that whatever was taken out was NOT replaced before the probability of the next event was calculated. This is DEPENDENT and the second probability has changed.

o In problems with multiple parts, each part uses the ORIGINAL NUMBERS in the problem! We are only finding probabilities, not actually removing, rolling, taking, etc. We are only trying to see how likely it is that something COULD happen.

For each problem, identify which type of probability question it is, write a probability statement, then find the probability.

1. A bag contains 26 tiles with the letters of the alphabet on them, one letter per tile. a. What is the probability that you reach in and choose one tile that has a vowel on it?

b. What is the probability that you reach in and choose one tile that has one of the letters in the word EQUATION on it?

c. What is the probability that you reach in the bag and choose one tile that has either a letter from the word EQUATION or a letter from the word NUMBER on it?

d. What is the probability that you reach in and pull out a vowel, replace the tile, and then pull out another vowel?

e. What is the probability that you reach in and pull out a vowel, you DO NOT replace the tile, then you reach in and pull out another vowel?

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You try!2. A box contains different colors of ping pong balls. There are 7 red, 12 purple, 5 green, 3 yellow and 3 white balls.

a. What is the probability of reaching in the box and grabbing a purple ball?

b. What is the probability of reaching in the box and pulling out a red ball, then a green ball, without replacement?

c. What is the probability of reaching in the bag and pulling out a red ball, then another red ball, then a yellow ball, with replacement?

d. What is the probability of reaching in the bag and pulling out a red ball, then another red ball, then a yellow ball, without replacement?

e. What is the probability of reaching in the bag and pulling out a white ball or a green ball?

f. What is the probability of reaching in the bag and pulling out a ball that is a primary color?

3. A bag contains 10 tiles numbered 1-10. a. What is the probability of reaching in the bag and choosing an even number or a number greater than 5?

b. What is the probability of reaching in the bag and choosing a number less than 4, and then reaching in and choosing another number less than 4, without replacement.

c. What is the probability or reaching in the bag and choosing and odd number?

d. What is the probability of reaching in the bag and choosing a multiple of 3, and then reaching in and choosing an even number, with replacement?

e. What is the probability of reaching in and choosing a multiple of 3 or an even number?

f. What is the probability of reaching in and choosing a number less than 4 or a number greater than 5?

4. A die is rolled once. What is the probability that the number rolled is greater than 2 and even?

5. Three storage bins contain colored blocks. Bin 1 contains 15 red and 15 blue blocks. Bin 2 contains 16 white and 15 blue blocks. Bin 3 contains 15 red and 15 white blocks. One block is randomly chosen from each bin. What is the probability that a red is chosen from bin 1, and blue is chosen from bin 2 and a white is chosen from bin 3?

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1. William drops a box of legos on the floor in the living room and leaves them. The box contained 25 red, 20 blue, 30 green, 17 white, 24 yellow and and 9 black legos. His sister comes in later and does not notice the legos all over the floor. She steps on a lego, begins to hop around in pain and then steps on a second lego. At this point she cannot walk because of the pain in both feet. What is the probability that she first steps on a red lego and then steps on a white lego?

2.

3. A classroom bookshelf contains 10 mysteries, 5 biographies, 8 thrillers and 2 science fiction novels. Simone, James and Kianna do not have anything to read during silent sustained reading time. What is the probability that Simone will choose a mystery, James will choose a biography and Kianna will choose a thriller?

For #4-6, five years after 650 high school seniors graduated, 400 had a college degree and 310 were married. 200 of the students with college degrees were married. Hint: a venn diagram may be helpful.4. What is the probability that a student has a college degree or is married?

5. What is the probability that a student has a college degree or is not married?

6. What is the probability that student does not have a college degree or is married?

7. Using a 6-sided die, what is the probability of rolling an even number or a number greater than 3?

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Day 7 Classwork Name_______________________________

1. There are 2400 subscribers to an Internet service provider. Of these, 1200 own Brand A computers, 500 own Brand B, and 100 own both A and B. What is the probability that a subscriber selected at random owns either Brand A or Brand B?

2. Below are the counts (in thousands) of earned degrees in the U.S. in a recent year, classified by level and by the sex of the degree recipient. One person is selected at random, find the following probabilities.

Bachelors Masters Professional Doctorate TotalFemale 616 194 30 16 856Male 529 171 44 26 770Total 1145 365 74 42 1626

a) P(female) b) P(Masters)

c) P(female and doctorate) d) P(male and bachelors)

e) P(masters or professional) f) P(female or bachelors)

g) P(male or female) h) P (bachelors or male)

3. Sylvia has a stack of playing cards consisting of 10 hearts, 8 spades, and 7 clubs. If she selects a card at random from this stack, what is the probability that it is a heart or a club?

4. Using a 6-sided die, what is the probability of rolling a 2 or a 5?

5. Using a 6-sided die, what is the probability of rolling an odd number or a number greater than 4?

6. A bag contains 4 blue, 3 red, and 2 yellow marbles. If a marble is randomly selected, what is the probability of selecting a red or a blue marble?

7. Using a 6-sided die, what is the probability of rolling at least a 2?

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Foundations of Math 2 – Unit 7: ProbabilityDay 8 – Practice

Warm-Up1. The Country of Transam is getting ready to select participants for the annual “Starving Games.” In District 24 there are a total of 2000 entries. Penny has 10 entries, Bernadette has 200 entries and Leonard has 400 entries.a) What is the probability that Penny’s entry will be selected?

b) What is the probability that Penny’s entry will not be selected?

c) What is the probability that either Bernadette’s entry or Leonard’s entry will be selected?

2. The table below shows the results of classes being asked for their favorite pet:Dogs Cats Birds Total

Boys 46 24 10 80Girls 30 42 8 80Total 76 66 18 160

a) What is the probability of selecting someone who likes dogs?

b) What is the probability of selecting a girl who likes cats?

c) What is the probability of selecting someone who likes cats or someone who likes birds?

d) What is the probability of selecting a boy or someone who likes dogs?

e) What is the probability of selecting a girl or someone who likes birds?

3. In Timmy’s school there are 300 people in the 11th grade. Currently 200 11th graders are taking English, 160 11th graders taking US History, and a total of 80 11th graders are taking both.a) What is the probability of selecting an 11th grader who is taking English?

b) What is the probability of selecting an 11th grader who is taking either English or US History?

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1. Three coins are tossed one after the other. a) List the sample space for the three flipped coins

b) Find the probability getting exactly 2 heads

c) Find the probability of getting at least 2 heads

2. Shannon did a survey of the students in her classes about whether they liked to get a brownie or a cookie as a special treat. She asked all 90 students in the class. 53 wanted a brownie, 21 wanted a cookie, and 11 wanted both. If Shannon were to select a student at random:a) What is the probability that they wanted a brownie or a cookie?

b) What is the probability that they did not want either a brownie nor a cookie?

3. If you choose a number 1-10, what is the probability of choosing an even number and a number greater than 8?

4. If you choose a number 1-10, what is the probability of choosing an even number or a number greater than 8?

5. At Fowlerville High School there are a total of 36 people who are enrolled in English III, a total of 48 people who are enrolled in U.S. HIstory, 12 people who are enrolled in English III and U.S. History, and 15 people who are not enrolled in either English III or U.S. History. Fill in the venn diagram for the information that is given.

On a bookcase there are 4 mystery books, 3 romance books, 2 sci-fi books, and 1 non-fiction book.6. List the sample space for drawing a marble from the bag.

7. What is the probability of picking a mystery book from the bookcase?

8. What is the probability of picking a sci-fi book from the bookcase?

9. What is the probability of picking a romance or a mystery book from the bookcase?

10. What is the probability of picking a book that is not a romance book?

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Foundations of Math 2 – Unit 7: ProbabilityDay 9 - Conditional Probability

Warm-Up

1. A bag has 26 tiles (one for each letter of the alphabet). a. What is the probability of reaching in the bag and choosing a tile with one of the first 10 letters of the alphabet OR a vowel?

b. What is the probability of reaching in the bag and choosing a tile with one of the first 10 letters of the alphabet AND a vowel?

2.a)Larry tosses a coin 60 times. It lands on heads 37 of those times. What is the experimental probability that the coin lands on heads?

b) What would the theoretical probability of the coin landing on heads be?

3. Determine if the following are mutually exclusive or mutually inclusive.a) Choosing a mother or choosing a teacher_______________________

b) Choosing a boy or choosing a girl________________

c) Choosing a vowel or a letter from the word PARTY______________

d) choosing a vowel or a letter from the word SPRY________________

4. Determine if the following are independent or dependent.a) Choosing an 8 from a deck of cards, replacing it, and choosing a jack__________________

b) Choosing a Queen from a deck then choosing an 8 without replacement___________________

c) Rolling a 6 on a die and rolling a 2 on another die_______________

d) Rolling 2 dice and getting a sum of 11___________________

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Guided Notes: Conditional Probability

Conditional Probability: the probability of a ________________________ occurring, given that a __________________has already occurred.

Examples of conditional probability:

The conditional probability of A given B is expressed as ___________________________

#1. The table below lists the number of each type of clothing Donna and Carol own.T-shirts Tank Tops Sweaters Dresses Total

Donna 15 10 4 6Carol 12 8 8 18Totala) What is the probability that Carol wears a dress?

b) What is the probability that Donna wears a tank top?

#2. Michelle’s purse is a mess. It has 3 packs of gum, 4 tubes of lipstick, 2 things of nail polish, 5 hair ties, and a candy bar. What is the probability that Michelle is able to pull out a pack of gum, given that she has already taken out the candy bar?

#3. Use the table below.Football Hockey Basketball Baseball Total

Boston 100 40 60 80Detroit 60 50 40 50Total

a) What is the probability that someone likes football, given that they are from Detroit?

b) What is the probability that someone is from Boston, given that they like basketball?

c) What is the probability that someone likes hockey, given that they are from Boston?

d) What is the probability that someone is from Detroit, given that they like baseball?

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#4. Kevin has 7 black socks, 4 gray socks, and 4 tan socks in his dresser drawer. What is the probability that he is able to pull out a black sock, given that he has already pulled out a black sock?

#5. Use the table below.Nuclear Bombs Death Rays Rocket

LaunchersKiller Robots Total

Active 4 5 12 40Disabled 6 10 18 160

Totala) What is the probability that it is disabled, given that it is a Death Ray?

b) What is the probability that it is a Rocket Launcher, given that it is disabled?

c) What is the probability that it is disabled, given that it is a Nuclear Bomb?

d) What is the probability that it is a Killer Robot, given that it is active?

#6. Bobby is trying to get into his house but it is dark outside and he cannot find his keys. His key ring has 4 round keys, 3 square keys, and 5 trapezoid keys. What is the probability that he picks the house key, given that is is a square key?

#7. Use the table below.Snakes Dogs Cats Lizards Total

North America 3 20 15 5South America 12 10 5 10

Totala) What is the probability that someone is in North America, given that they own a dog.

b) What is the probability that someone owns a snake, given that they live in South America?

c) What is the probability that someone owns a lizard, given that they live in North America?

d) What is the probability that someone is in South America, given that they own a cat?

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e) If a person is chosen at random, what is the probability that they own a dog?

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Name_______________________________#1. The table below shows the employment status of individuals in a particular town by age group.

Full Time Part Time Unemployed Total0-17 24 164 371

18-25 185 203 14826-34 348 67 2735-49 581 179 10450+ 443 162 173

Totala) If a person in this town is selected at random, find the probability that the individual is employed part-time, given that he or she is between the ages of 35 and 49.

b) If a person in the town is randomly selected, what is the probability that the individual is unemployed, given that he or she is over 50 years old?

c) A person from the town is randomly selected. What is the probability that the individual is employed full time, given that he or she is between 18 and 49 years old?

d) A person from the town is randomly selected. What is the probability that the individual is employed part time, given that he or she is at least 35 years old?

#2. The following table shows the results of a survey of 2000 gamers about their favorite home video game systems, organized by age group. If a survey participant is selected at random, determine the probability of each of the following.

Playstation 3 Xbox 360 Wii Computer Total0-12 63 84 55 51

13-18 105 139 92 11319-24 248 217 83 16925+ 191 166 88 136

Totala) The participant prefers the Playstation 3.

b) The participant prefers the Xbox 360, given that the person is between the age of 13 and 18.

c) The participant prefers Wii, given that the person is between the ages of 13 and 24.

d) The participant is under 12 years of age, given that the person prefers a computer.

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#3. A snack-size bag of M&Ms candies is opened. Inside there are 12 red candies, 12 blue, 7 green, 13 brown, 3 orange, and 10 yellow. Three candies are pulled from the bag in succession, without replacement.a) Determine the probability that the first candy drawn is blue, the second is red, and the third is green.

b) Determine the probability that the third candy is green, given that the first 2 were blue and red.

#4. Suppose we survey all the students at school and ask them how they get to school and also what grade they are in. The chart below gives the results. Complete the two-way frequency table:

Bus Walk Car Other Total9th or 10th 106 30 70 411th or 12th 41 58 184 7Total

Suppose we randomly select one student.a. What is the probability that the student walked to school?

b. P(9th or 10th grader)

c. P(rode the bus OR 11th or 12th grader)

d. What is the probability that a student is in 11th or 12th grade given that they rode in a car to school?

e. What is P(Walk|9th or 10th grade)?

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Foundations of Math 2 – Unit 7: ProbabilityDay 10 - Conditional Probability

Warm-Up

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The following table shows the counts of earned degrees for several colleges on the East Coast. The level of degree and the gender of the degree recipient were tracked.

Bachelor’s Master’s Professional Doctorate TotalFemale 542 128 26 18Male 438 165 38 20Totala) What is the probability that a randomly selected degree recipient is a female?

b) What is the probability that a randomly chosen degree recipient is a man?

c) What is the probability that a randomly selected degree recipient is a woman, given that they received a Master’s Degree?

d) For a randomly selected degree recipient, what is P(Bachelor’s Degree| Male)?

Animals on the endangered species list are given in the table below by type of animal and whether it is domestic or foreign to the United States. Complete the table and answer the following questions.

Mammals Birds Reptiles Amphibians TotalUnited States 63 78 14 10

Foreign 251 175 64 8

If an endangered animal is selected at random, what is the probability that:a) it is a bird found in the United States?

b) it is foreign or a mammal?

c) it is a bird, given that it is found in the United States?

d) it is a bird, given that it is foreign?

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Day 10 Classwork Name_____________________The questions “Do you play football?” was asked of 110 students. Results are shown in the table.

Play football Don’t play football TotalBoys 42 75Girls 23Total 54 110

1. What is the probability of randomly selecting an individual who is a boy and who plays football?

2. What is the probability of randomly selecting an indidual that is a boy?

3. What is the probability of randomly selecting an individual that plays football?

4. If you randomly select a boy, what it the probability they play football?

5. If you randomly select a football player, what is the probability that they are a boy?

At a mall, 100 people were surveyed and were asked if they owned a home.Yes No Total

Male 41 19Female 28 12

Total6. What is the probability of selecting an individual who is a male who owns a home?

7. What is the probability of randomly selecting a female?

8. What is the probability that an individual is a female, given that they own a home?

9. What is the probability that an individual does not own a home, given that they are male?

10. What is the probability that someone is a male, given that they do not own a home?

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Foundations of Math 2 – Unit 7: ProbabilityDay 11 - Practice

Warm-Up

1. Use the table below to answer the questions

Games Roller Coasters Attractions TotalChildren 60 120Adults 80 130Total 70 95 85

a. Probability of selecting someone who likes Roller Coasters?

b. Probability of selecting an adult given that they like the attractions?

c. Probability of selecting someone who likes roller coasters given that they are an adult?

2. Monica has 6 pink socks, 8 white socks, and 4 blue socks. What is the probability of Monica selecting a blue sock given that she has already picked out a blue sock?

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1. There are 5 white balls, 8 red balls, 7 yellow balls and 4 green balls in a container. A ball is chosen at random.a) P(red)

b) P(red or white)

c) P(neither red not green)

d) P(not yellow)

e) P(black)

2. A coin is tossed. a) List the sample space

b) P(heads)

c) P(heads or tails)

d) P(neither heads nor tails)

3. A die is rolled.a) List the sample space

b) P(even)

c) P(prime)

d) P(odd and prime)

4. A month is chosen from a year.a) P( selecting a month with 31 days)

b) P(selecting a month that ends in Y)

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c) P(selecting a month that ends in R)

d) P(selecting a month that starts with J or ends in Y)

e) P(selecting a month that starts with J and ends in Y)

5. There are 25 students in the 5th grade. 15 are boys and the rest are girls. A student is selected for a field trip at random.a) P(selecting a boy)

b) P(selecting a girl)

c) Odds in favor of a boy

d) Odds in favor of a girl

e) Odds against boys

6. In a class of 24 students, 10 take Biology, 12 take Chemisty, and 3 take both Biology and Chemistry. Find the probability that a student picked at random from the class takes:a) Chemistry, but not biology

b) Chemistry or Biology

c) Biology, but not chemistry

d) Biology and Chemistry

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REVIEW GUIDE ------Foundations of Math 2 – Unit 7: Probability

Warm-Up

1. You toss a coin, roll a 6-sided die, and spin a 5 sectioned spinner. How many outcomes would there be in the sample space?

2. In one hour yesterday, 2 out of every 5 meals sold was a kid’s meal. Based on the findings, how many kids meals can we expect to sell if 860 total meals are sold?

3. A spinner is divided into 8 equal sections, numbered 1-8. What is the probability that it will land on a 3 or a number greater than 6?

4. Julie has 10 blue pencils numbered 1-10 and 6 red pencils numbered 11-16 in her pencil case. a) What is the probability she picks a blue pencil or an even numbered pencil?

b) She randomly chooses 3 pencils without replacement. What is the probability that she chooses 2 blue pencils in a row, followed by a red pencil?

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Counting Principle: How many different combinations can be made?

1. Meal Choices: 6 types of pop (soda), 3 salads, 4 sandwiches, 2 desserts

Find the probability. Using a die.2. P (odd ) 3. P (4) 4. P (1,2,3,4,5,or 6)

Find the probability.Using the spinner.5. P (2) 6. P(1 or 2) 7. P (6)

Using a coin first and then a die. Write each answer as a fraction.8. List the sample space

9. P (tail, 4) 10. P (tail, odd #) 11. P (tail, 0)

There are eleven marbles in a bag. Four are red, six are white, and seven are blue. Find each probability if you select one marble from the bag. 12. P (not white) 13. P (red) 14. P (blue or white)

Suppose there are 12 marbles in a bag. Four are solid, six are multi-colored, and two are clear. Find each probability if you reach in and select two marbles replacing them after each pick.

15. P (clear then solid) 16. P (solid then solid) 17.P(multi, multi, then clear)

Independent or Dependent. Circle the answer.18. A coin toss landing heads and a number cube coming up a five. Independent or Dependent

19. Suppose you draw a tile, and then draw another tile replacing the first. Independent or Dependent

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1 2

2 3

20. Below, draw a tree diagram to show the number of outcomes for the given situation. You are going to a diner and get to pick from 4 sandwiches (cheeseburger, chicken, ham, turkey) and 2 sides (french fries, chips). After completing the sample space, write how many outcomes there are to choose from for lunch.

21. John asked 100 people which type of music they enjoyed. The results are below.

One person is picked at random.

a. What is the probability that the person enjoys Classical?b. Given that the person is a women, what is the probability that she likes Rock? c. Given that the person is a man, what is the probability that they like Folk music?

22. 1200 people were surveyed about their body image. The results are below.

One person is picked at random.

a. Given that a male is selected, what is the probability that he thinks he is overweight?b. Given that a female is selected, what is the probability that she thinks she is underweight?c. Given that a female is selected, what is the probability that she thinks she is about right?

23. Of the people with black hair, 7 have brown eyes, 2 have blue eyes, 2 have hazel eyes, and 1 has green eyes.Of the people with brown hair, 12 have brown eyes, 5 have hazel eyes, 3 have green eyes, and 8 have blue eyes.Of the people with blonde hair, 9 have blue eyes, 1 has brown eyes, 1 has hazel eyes, and 2 have green eyes.Of the people with red hair, 1 has hazel eyes, 1 has green eyes, 2 have blue eyes, and 3 have brown eyes.

Use the information from above to fill in the two-way frequency table below.Hair Color

Black Brown Red Blonde Total

Eye

Colo

r BrownBlueHazelGreenTotal

a. Given that a member of the team has blue eyes, what is the probability that he/she has:Brown hair? Blonde hair?

b. Given that a member of the team has brown hair, what is the probability that he/she has:

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Hazel eyes? Doesn’t have green eyes?

c. Given that a member of the team has black hair, what is the probability that he/she has:Blue eyes? Brown eyes?

d. What is the probability a member of the team has brown hair? Blue eyes?

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