ms. campos - math 7 unit 11 probability 2017-2018
TRANSCRIPT
Ms. Campos - Math 7
Unit 11 – Probability
2017-2018
Name: _____________________________ #______
Date Lesson Topic Homework
F 5 3/9 1 Outcomes Lesson 1 – Page 5
M 6 3/12 2 Probability of Simple Events Lesson 2- Page 10
T 1 3/13 3 Probability of Independent Events Lesson 3 – Page 13
W 2 3/14 4 Probability of Dependent Events Lesson 4 – Page 16
T 3 3/15 Activity Study!
F 4 3/16 Quiz Enjoy the weekend!
M 5 3/19 5 Experimental Probability Lesson 5 – Page 19
T 6 3/20 Review Finish Review and Study!
W 1 3/21 Test
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Unit 11 -Lesson 1
Aim : I can determine Outcomes (Tree Diagrams and Fundamental Counting Principle)
Warm up: Copy down the following vocabulary words.
Vocabulary:
Outcomes: ________________________________________________________________________________
Sample Space: _____________________________________________________________________________
Fundamental Counting Principle: ______________________________________________________________
Outcomes of Flipping a Coin 2 times
Outcomes of Sandwich Choices
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Guided Practice:
Tree Diagrams:
1. Make a tree diagram to represent the sample space of flipping a coin and rolling a fair die.
Total Outcomes: _______
2. A pizza shop offers the following options for a slice of pizza:
1. TYPE: Regular or Sicilian
2. CRUST: Thin or Thick
3. TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies
Make a tree diagram to represent the sample space of the various slices that could be made.
Total Outcomes: _______
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Fundamental Counting Principle:
3. A pizza shop offers the following options for a slice of pizza:
1. TYPE: Regular or Sicilian
2. CRUST: Thin or Thick
3. TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies
Use the FCP to determine the total number of possible slices of pizza.
4. A restaurant has four different appetizers, three different entrees, and two different desserts on their price-
fixed menu. How many different outcomes can there possibly be?
5. If a student rolls two dice, what is the number of total outcomes?
5
Problem Set:
1. At a birthday party, the guests get to create their own sundae. They can choose one flavor of ice cream, one
type of syrup, and one topping.
1. Flavor: Vanilla or Chocolate
2. Syrup: Hot Fudge, Caramel, or Peanut Butter
3. Topping: Sprinkles, Marshmallows, or Cherry
Make a tree diagram to represent the sample space of the various sundaes that could be made.
2. If Mr. Stinson has fifteen pairs of pants, twenty-three collared-shirts, and sixty-four ties; what are the total
number of outfits that he can possibly create?
3. Find the total number of different outfits that can be made from the following:
3 different sweaters, 4 turtlenecks, and 2 pairs of jeans
4. When rolling a fair die and flipping a coin, what are the total possible outcomes?
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Unit 11- Lesson 1 - Homework
1. Create a tree diagram and list the sample space
representing all possible outcomes of flipping a
coin twice.
2. Create a tree diagram and list the sample space
representing all possible outcomes of choosing a
hat that comes in black, red, or white AND
medium or large.
3. Create a tree diagram and list the sample space
representing all possible outcomes of rolling a
fair die twice.
4. Create a tree diagram and list the sample space
representing all possible outcomes of choosing
peach or vanilla yogurt topped with peanuts,
chocolate, strawberries, or granola.
5. At a wedding you can choose from 4 different
meats (lobster, steak, chicken, or pork). You
can choose from 2 side dishes (pasta or
vegetables) and from 2 desserts (fruit or ice
cream). How many total outcomes are possible?
Use the FCP.
6. At dinner you have the choice of 3 different
soups, 4 appetizers, 5 main meals, and 3
desserts. Find the number of possible outcomes
of choosing 1 of each course from the menu.
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Unit 11 -Lesson 2
Aim: I can deterine probability of simple events
Warm up: At dinner you have the choice of 3 different soups, 4 appetizers, 5 main meals, and 3 desserts. Find
the number of possible outcomes of choosing 1 of each course from the menu.
Vocabulary:
Probability: The chance that some event will happen; the ratio of ways a specific event can happen to the total
number of outcomes.
𝑃(𝑒𝑣𝑒𝑛𝑡) = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
*Probability can be expressed as a fraction, a decimal, or a percentage.*
Complementary Events: the set of all outcomes in the sample space that are not included in the event.
Example: Rolling a 3 on a number cube is 1/6, the complement is 5/6 (numbers 1, 2, 4, 5, 6).
P(event) + P(complement) = 1
Probability of a certain event: _________ Probability of an event not occurring: _________
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Guided Practice:
1. A fair coin is flipped, what is the probability of getting a ‘tails’?
Fraction___________ Decimal__________ Percent___________
2. The probability that it rains today is 60%. What is the probability that it does not rain?
Fraction___________ Decimal__________ Percent___________
3. A spinner consists of six equal sections numbered 1-6.
a) What is the probability of the spinner landing on 5? b) Find P(3).
c) What is the probability of getting an even number? d) What is P(3 or 4)?
e) What is the probability of the spinner landing on 7?
4. John has eight red marbles and four blue marbles in a jar. What is the probability that John picks a marble at
random, and it is not red?
5. What is the sum of the probabilities of all the outcomes in a sample space?
6. The probability of a certain event occurring is 1
4 .
a) Express this probability as a decimal. b) Express this probability as a percentage.
c) What is the probability that this event does not occur?
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7. Which of these cannot be considered a probability of an outcome? Explain.
[A] 1
3 [B] -0.59 [C] 1 [D] −
1
5 [E] 0
[F] 1
2 [G] 0.80 [H] 1.45 [I] 112% [J 100%
Describe each event as impossible, likely, unlikely, or certain.
8. The probability of tossing a number cube and getting 5 is 6
1. _________________
9. The probability of spinning blue on a spinner is 0. ___________________________
10. The probability of selecting a red marble from a bag of marbles is 0.47. ____________________
11. The probability of selecting a tile with a vowel on it from a box of tiles is 20
3. ________________
Problem Set:
1. If a fair die is rolled one time, find the probability of the following outcomes:
[a] rolling a four
[b] rolling an even number
[c] rolling a number greater than four
[d] rolling a number less than seven
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2. A box contains 5 green pens, 3 blue pens, 8 black pens, and 4 red pens. One pen is picked at random.
[a] What is the probability the pen is green?
[b] What is the probability the pen is blue or red?
[c] What is the probability the pen is gold?
3. The spinner is used for a game. Write each probability as a fraction.
[a] P(3)
[b] P(5)
[c] P(1 or 2)
[d] P(odd)
[e] P(a number less than 5)
2 1
3 4
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Unit 11 Lesson 2 – Homework
1. A spinner with six equal sections is used for a game. The sections are numbered 1-6.
Write each probability as a fraction.
a. P(3) b. P(7) c. P(3 or 4) d. P(even) e. P(not 5)
2. A bag contains 4 red marbles, 3 orange marbles, 7 green marbles, and 6 blue marbles.
Express each probability as a fraction:
a. P(red) b. P(green) c. P(red or blue) d. P(not green) e. P(purple)
3. If the probability that it will snow tomorrow is 0.85, what is the probability that it will not snow tomorrow?
4. There is a 30% chance that it will rain on Saturday. What is the probability that it will not rain?
5. A weather forecast states that there is an 80% probability of rain tomorrow. Which term best describes the
likelihood of rain tomorrow?
A. Impossible B. Unlikely C. Likely D. Certain
6. A company that manufactures light bulbs finds that one out of every twenty light bulbs is defective.
a. Express, as a fraction, the probability that a random light bulb is defective.
b. Express, as a fraction, the probability that a random light bulb is not defective.
c. In a sample of 100 light bulbs, how many bulbs should the company expect to be defective?
d. The manager of your branch of the company tells you that 20% of the light bulbs manufactured are
defective. Is this an accurate statement?
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Unit 11 - Lesson 3
Aim: I can determine probability of Independent Events
Warm up: There is a 30% chance that it will rain on Saturday. What is the probability that it will not rain?
Important Vocabulary:
Compound Event: _________________________________________________________________________
Independent Event: ________________________________________________________________________
Dependent Event: ________________________________________________________________________
Guided Practice: Determine if each of the following events are considered independent or dependent:
[A] Tossing a coin and drawing a card from a deck.
[B] Drawing a marble from a jar, not replacing it, and then drawing a second marble.
[C] Driving on ice and having an accident.
[D] Having a large shoe size and having a high IQ
[E] Not studying for a test and receiving a low test score.
[F] Picking a card from a deck, replacing it, and choosing another card.
[G] Picking a card from a deck, and then choosing another card without replacing the first.
[H] Picking a marble from a jar, replacing it and picking another marble.
[I] Committing a crime and getting arrested.
[J] Not eating dinner and being hungry at 8:00 pm.
[K] The Giants winning the Super Bowl and the Rangers winning the Stanley Cup.
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Find the probability of compound independent events
Rule: multiply the probability of each event.
𝑷(𝑨 𝒂𝒏𝒅 𝑩) = 𝑷(𝑨) × 𝑷(𝑩)
1. When flipping a coin twice, what is the probability of getting two tails?
2. A game calls for the player to flip a coin and then roll a fair die. Find each probability:
[A] P(tails and 4) [B] P(heads and odd) [C] P(tails and 7)
Problem Set:
1. There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is
selected at random, replaced, and another is selected. Find the following probabilities.
[a] P(green and blue) [b] P(red and orange) [c] P(red and yellow)
[d] P(two blue marbles) [e] P(no red marbles) [f] P(red or blue, and green)
2. An arrangement of 8 students is shown. The numbers of all the students are in a basket. The teacher selects
a number and replaces it. Then the teacher selects a second number. Find each probability.
[A] P(student 1, then student 8) =
[B] P(student in row A, then student in row B) =
[C] P(student in row A, then student 6, 7, or 8) =
Row Student
A 1 2 3 4
B 5 6 7 8
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Unit 11- Lesson 3 – Homework
1. A spinner has eight equal sections numbered 1-8. The spinner is spun twice. Find the following
probabilities:
[a] P(1 and 2) [b] P(3 and 3) [c] P(odd and even) [d] P(1 and not 1)
[e] P(7 and 0) [f] P(1 and 0) [g] P(not 0 and not 7) [e] P(both numbers < 4)
2. A company produces two different sized light bulbs. One out of every 25 big bulbs is defective. One out of
every 50 small bulbs is defective.
[a] What is the probability that when purchasing one of each, both will be defective?
[b] What is the probability that when purchasing only one small bulb, the bulb will not be defective?
[c] In a sample of 200 big bulbs, how many defective bulbs are to be expected?
[d] In a sample of 200 small bulbs, how many defective bulbs are to be expected?
3. What is the probability of flipping a coin 3 times and getting heads every time?
4. What is the probability of getting five consecutive tails when flipping a coin five times?
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Unit 11- Lesson 4
Aim: I can determine probablity of Dependent Events
Warm up: What is the probability of flipping a coin 3 times and getting tails every time?
To find the probability of compound dependent events, multiply the probability of the first event
and the probability of the second event after the first event happens.
𝑷(𝑨 𝒂𝒏𝒅 𝑩) = 𝑷(𝑨) × 𝑷(𝑩 𝒂𝒇𝒕𝒆𝒓 𝑨)
Guided Practice:
1. There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is
selected at random, and then another is selected without replacement.
A) Find the probability that two blue marbles will be selected
Step 1: Find the probability of the first event happening:
P(first marble is blue) =
Step 2: Find the probability of the second event happening, assuming the first event did happen:
P(second marble is blue) =
Step 3: Multiply the probabilities of each event:
P(two blue marbles) =
B) Find the probability that the first marble will be red and the second will be green without replacement:
P(Red and then Green) =
C) Find the probability that the first marble will be orange and the second will be blue without replacement:
P(Orange and then Blue) =
D) Find the probability that the first marble will be red and the second marble will be red:
P(two red marbles) =
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2. A mason jar contains eighteen marbles in the following colors:
[i] 6 green marbles
[ii] 4 blue marbles
[iii] 7 red marbles
[iv] 1 black marble
What is the probability of the following outcomes without replacement?
[a] P(green and then blue) [b] P(two reds)
[c] P(black and then black) [d] P(two blacks)
[e] P(red and then green) [f] P(black and then not black)
[g] P(green and then not red) [h] P(two blues)
Problem Set:
1. A student writes the numbers (1-9) on index cards, and then places them in a hat. If another student draws
two cards without replacing them, what is the probability of:
[a] P(8 and then 5) [b] P(both digits being even)
[c] P(both digits being odd) [d] P(both digits being perfect squares)
[e] P(1 and then 2) [f] P(9 and then a number less than 9)
[g] P(both numbers greater than 5) [h] P(both numbers are prime)
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Unit 11 Lesson 4 - Homework
1. Mr. Murphy has to select two students from class to join the SLAM. He decides to choose randomly from
a class of eleven girls and nine boys.
[A] What is the probability that he will choose a girl first and then a boy second?
[B] What is the probability he will choose a boy first and then a girl second?
2. There were 5 cards in a bag labeled 0 through 4. Find each probability if two cards are picked with no
replacement.
[a] P(2 and then 4) [b] P(2 and then 2)
[c] P(1 and then 2 and then 3) [d] P(prime # and then 0)
[e] P(three 0’s) [f] P(# less than 2 and then a 4)
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Unit 11 - Lesson 5
Aim: I can determine Experimental Probability
Warm up: Copy down the following vocabulary words.
Important Vocabulary:
Theoretical Probability: ______________________________________________________________________
Experimental Probability: ____________________________________________________________________
Guided Practice:
Theoretical Example:
1. A fair coin is flipped four times.
[a] What is the probability that the first flip will be heads?
[b] What is the probability that all four flips will be tails?
[c] How many times would you expect to get tails in the four flips?
[d] If you were to flip the coin a total of 100 times, how many times would you expect heads to appear?
Experimental Example:
2. A probability experiment is conducted. In the experiment, a fair coin is flipped 20 times. The results are
displayed in the graph below:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 T
H X X X X X X X X X X X X 12
T X X X X X X X X 8
[a] What is the experimental probability of flipping heads?
[b] What is the experimental probability of flipping tails?
[c] How could you make this experiment more representational of the theoretical probability? (how can
this be more accurate?)
[d] According to this experiment, how many times would you expect to get heads in 100 flips?
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Problem Set:
1. A probability experiment is conducted to find the experimental probability of getting various sums when
two number cubes are rolled. The results of 50 rolls are shown below:
[a] According to the experiment, what is the experimental probability of rolling a sum of 9?
[b] What is the experimental probability of rolling a sum of 8?
[c] What is the experimental probability of rolling a sum that is greater than 7?
[d] What is the experimental probability of rolling a sum that is greater than or equal to 7?
[e] Which sum is most likely to appear based on the experiment?
[f] Which sums are least likely to appear?
[g] In this experiment, two number cubes were rolled. What is the theoretical probability of getting two 3s? Is
this the only way to get a sum of 6?
[h] Why is it that certain sums are more likely to appear than others?
[i] Why is it impossible to roll a 1?
0
2
4
6
8
10
12
2 3 4 5 6 7 8 9 10 11 12
Results
Sum
# of
rolls
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Unit 11 Lesson 5 – Homework
1. If a student flipped a coin one hundred times and the coin landed on heads 61 times:
[A] What is the Experimental Probability of flipping a Tails?
[B] What is the Theoretical Probability of flipping a Tails?
[C] Compare the two probabilities
2. How many heads would you expect when flipping a fair coin fifty times?
3. How many primes would you expect when rolling a fair die one hundred times?
4. How many times would you expect to roll a 5 when rolling a fair die twelve times?
5. The odds of a particular team to win the Super Bowl are 1/8. If these odds stayed consistent every year,
how many super bowl titles would you expect this team to have in the next 80 years?
6. A fair die is rolled twice.
[a] How many possible outcomes are there?
[b] What is the probability of rolling a 3 and then a 5?
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7. A company that produces car parts tests a sample of fifty parts. After testing all fifty parts, they find that 7
parts are defective.
[a] What is the experimental probability of a part being defective?
[b] What is the experimental probability of a part being functional?
[c] How many defective parts would you expect in a batch of 1000 parts?
[d] How could the company find a more accurate representation of their defective parts?
8. A particular game of chance is played by flipping a coin and rolling a fair die What is the probability of
winning the game if:
[a] Winning means (heads, one)
[b] Winning means (tails, odd)
[c] Winning means (heads, prime)
[d] What is the total number of possible outcomes for this game?
[e] Which of these games is a player most likely to win?
9. The Judicial Committee at a college consists of two administrators, four faculty members, four seniors,
four juniors, two sophomores, and two freshmen. Suppose one committee member is selected at random.
Find the following probabilities.
[a] That a non-student is selected.
[b] That a senior or a junior is selected.
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7R Unit 11 Probability Review
Probability - A number between 0 and 1 that represents the likelihood that an outcome will occur.
Compound event - An event consisting of more than one outcome from the sample space of a chance
experiment.
Experimental probability - The ratio of the number of times the event occurs to the total number of trials.
In 1-10: Determine whether the events described are dependent or independent events.
1. Choosing two cards from a deck of cards without replacement. ______________________
2. Picking a marble from a jar, replacing it, and picking another one. ______________________
3. Rolling a die and flipping a coin. ______________________
4. Spinning a spinner twice. ______________________
5. Throwing a printer in the garbage, and not being able to print. ______________________
6. Choosing two marbles out of a jar, without replacement. ______________________
7. Picking a card, replacing it, and picking another card. ______________________
8. Studying and getting good grades. ______________________
9. Choosing a student from a class of 25, and picking another from the remaining 24 students. __________
10. Picking a pen from a box, replacing it, and picking another pen. ______________________
In 11-22: Use the diagram of a spinner to the right to answer the questions.
11. What is the probability of getting a 1?
12. What is the probability of getting a 2 or a 3?
13. P(odd)
14. P(even)
15. P(odd or even)
16. P(less than 3)
17. How many total outcomes are there for spinning the spinner twice?
18. Is spinning the spinner twice a compound independent event or compound dependent event?
19. P(1 and 1)
20. P(5 and 5)
5
2
6
3
1
4
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A jar contains 5 red marbles, 7 green marbles, 3 blue marbles, and 10 yellow marbles. In these compound event
problems, assume there is replacement.
21. P(red and then blue 22. P(red or blue, and then green) 23. P(Both Yellow)
A jar contains 5 red marbles, 7 green marbles, 3 blue marbles, and 10 yellow marbles. In these compound event
problems, assume there is no replacement.
24. P(both red) 25. P(red and yellow) 26. P(red and blue) 27. P(Both yellow)
28. The probability that it will rain tomorrow is 0.7. What is the probability that it will not rain?
29. The chance that a certain event does not occur is 40%. What is the probability that this event does occur?
30. How many times would you expect to get heads if you flipped a coin 400 times?
31. In a probability experiment, a coin is flipped 200 times. The coin landed on heads 73 times.
a. How many times did it land on tails?
b. What is the experimental probability of getting heads?
c. Based on experimental probability, how many heads would you expect in 400 flips?
d. Based on theoretical probability, how many heads would you expect in 400 flips?
32. Sam rolled a number cube 50 times. A 3 appeared 10 times. How many times would Sam expect a three
show up out of the 50 tosses?
33. A coin is tossed 60 times. 27 times head appeared. Find the experimental probability of getting heads.
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34. A coin is tossed 60 times. Heads appeared a total of 27 times. Find the experimental probability of getting
heads.
35. Joey works in a factory. The factory makes i-phones. Joey checks if the I-phones are in good working
condition. After checking the first 50 phones, he noticed that 8 of them are defective. Out of the 800
produced that day, how many phones can Joey expect to be defective?
36. A T-Shirt company gives the following options for a customized shirt.
Color: Red, Green, or Black
Size: Small, Medium, or Large
Sleeves: Short or Long
Construct a tree diagram, and list the sample space of all possible combinations
37. How many outcomes do you expect from the above experiment using the Fundamental Counting Principle?
38. What is the probability of having a Red, small Short sleeved T shirt?
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MIXED Review
39. Write as a percent 1/9. (Round to the nearest percent) 40. Solve 3x – 7 = 23
41. Simplify: 3(5x + 3) + 2(7 + 3x) 42. Simplify: 4(3x – 4) + 6(5x + 7)
43. Evaluate: 5x −2y, if x = 3 and y = −2 44. What is the constant of proportionality of y = 3x?
45. What is the unit rate of 5lbs for $15.85? 46. If the chance of snow is 0.01, is it likely to happen?
State the type sample the following are(Random, Systematic, Stratified or Convenient
47. Testing every 7th part. 48. Making groups of students based on grade.
49. Selecting the first 10 people you see to ask them questions.
50. Find the unit rate (Cost per pound of Deli Ham) 51. Graph the following on an inequality x < -2:
$35.40 for 5 pounds.