probability unit assignments - ms. turnbull's...

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Probability Unit ASSIGNMENTS

# Assignment Complete/Incomplete

Assignment 1: Applications of Probability

Assignment 2: Theoretical Probability

Assignment 3: Experimental Probability

Assignment 4: Compounding Independent Events

Assignment 5: Probability and Odds

Assignment 6: Expected Value

Probability Test:

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Assignment #1: Applications of Probability

1. Change the following decimals to percent.

.58 .02

.32 .985

2. Change the following percentages to decimal.

100% 2.45%

40% 66.5%

3. Place the following events on a probability scale.

a. You will live for 100 years.

b. In the first week of November, it will snow at least once in Winnipeg.

c. The sun will rise in the east tomorrow morning.

d. The next baby born in Victoria Hospital will be a girl.

e. You will get 80% or higher in this unit.

Impossible l---------------------------------------------------------------------l Certain

0 1

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4. The probability of winning a particular Lotto 6 / 49 is approximately 1 in

14 000 000. The probability of being hit by lightning once in your lifetime is

approximately 1 in 600 000. Are you more likely to win the lottery or be hit by

lightning?

5. The probability that a person is left-handed is 1 in 10 people. The city of

Winnipeg has a population of approximately 650 000 people. How many people are

left-handed in Winnipeg?

6. The probability of twins being born is 1:90. If during one year there were

15 500 births in a particular city, how many of those births would be twins?

7. The weather stations indicates that there is a 30% chance of rain on Tuesday.

What is the probability that it will not rain?

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Assignment #2: Theoretical Probability

1. Determine the probability of rolling each of these numbers with a fair six-sided

number cube:

a. The number 3

b. An odd number

c. A number greater than or equal to 2.

d. Not the number 5 or 6.

e. The number 0.

2. The diagram below shows a jar of jelly beans. The jelly beans are of the same

size and shape. You put your hand in to the jar and without looking select a jelly

bean. Express each probability as a fraction and as a percent of the following:

a. P (yellow)

b. P (Green)

c. P (Yellow or Green)

d. P (not black)

e. P (not white)

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3. Each letter of the word MATHEMATICAL is on a different card. All the cards

are the same size. The cards are placed face down and shuffled. What is the

probability that you will draw each of the following?

a. P (M)

b. P (A)

c. P (C, H, or L)

d. P (not T)

e. P (vowel)

4. What is the probability of spinning each of the following with the given spinner?

Express each probability as a fraction and as a percent.

a. P (red)

b. P (yellow)

c. P (red, yellow, or green)

d. P (neither red nor yellow)

e. P (not blue)

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5. What is the probability of drawing the following cards from a standard deck of

52 playing cards?

a. P (5 of clubs)

b. P (diamond)

c. P (red card)

d. P (ace)

e. P (a black 10)

6. There are 4 white, 14 blue, 6 green, and 1 yellow marbles in a bag. You put your

hand into the bag and without looking, select a marble. What is the probability of

removing the following?

a. P (white)

b. P (blue or green)

c. P (yellow)

d. P (not orange)

e. P (neither white nor blue)

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Assignment #3 Experimental Probability

1. Use the data from both experiments to show the experimental probabilities

for 120 rolls of the die. To find these probabilities, add the number of

times each event occurred in the first and second experiments and divide by

120.

i. The number 5

ii. An even number.

iii. A number greater than 4.

iv. Not the number 3.

v. The number 9.

2. Answer the following questions:

a) How closely did your experimental probability compare to the theoretical

probability on the first 60 rolls.

b) How closely did your experimental probability compare to the theoretical

probability on the second 60 rolls.

c) How closely did your experimental probability compare to the theoretical

probability for 120 rolls of the die.

d) Predict what would happen to these probabilities if you rolled the die

1000 times.

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Assignment #4 Probability (Compounding Independent Events)

1. Toss one coin and spin the given spinner.

a. Draw a tree diagram and list all possible outcomes.

b. Find the following probabilities.

P (Heads, Red)

P (Tails, Blue)

P (Tails, not Green)

2. A jar contains the following 4 marbles: 1 blue, 1 green, 1 red, and 1 yellow.

Students select two marbles from the jar. When the first marble is selected, it is

returned to the jar before the second marble is selected.

a. Draw a tree diagram and list all possible outcomes.

b. Find the following probabilities:

P (blue, blue)

P (red, yellow)

P (neither marble is green)

P (two the same color)

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3. Two dice are rolled. The numbers displayed on each die are added. What is the

probability of each of the following events? Refer to the table in example 2.

a. P (7)

b. P (12)

c. P (6 or 11)

d. P (> 10)

e. P (both dice display the same number)

f. P (sum is greater than 3 and less than 10)

4. Assume it is equally likely that a child is born a boy or a girl.

a. Draw a tree diagram and list the possible outcomes for a family of 2

children.

b. What is the probability that in a family of 2 children, both will be girls.

c. Extend the tree diagram and list the possible outcomes for 3 children.

What is the probability that in a family of 3, all will be boys?

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5. A pair of dice are tossed. The results are multiplied with one another.

a. Draw a table to list all possible outcomes.

b. What is P (even number)

c. What is P (≥ 20)

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Assignment #5 Probability and Odds

1. The odds against a hockey team winning a game are 2 : 9. What is the

probability that the team will win a game?

2. Nathan plays basketball. He has scored on 2 out of 10 shots. He says that his

odds against scoring are 4 to 1. Do you agree? Explain.

3. Each letter of the word MATHEMATICAL is written on a different card and

placed face down on a table.

a. Determine the probability of drawing an “M”.

b. Determine the odds in favor of drawing an “M”.

c. Determine the probability of not drawing an “M”.

d. Determine the odds against drawing an “M”.

4. Susan works at an appliance store in Brandon. The odds that a new vacuum

cleaner will need repairs in the first 4 years are 1 : 3.

a) What is the probability that a new vacuum cleaner will need repairs?

b) Is this a good vacuum cleaner in your opinion?

c) If the vacuum cleaner cost $350 and the manufacturer gave a 4 year warranty

that cost $50, would you buy the warranty? Why or why not?

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5. A die is rolled. Find the following:

a. The probability of rolling a number greater than two.

b. The odds in favor of rolling a number greater than two.

c. The probability of not rolling an even number.

d. The odds against rolling an even number.

6. In a class of 32 students, 18 students take an Art option, 10 other students

take a Drama option, and the rest of the students take a Choir option. One

student is selected at random. Find the following:

a. The odds in favor of the selected student taking Drama.

b. The odds against the selected student taking Choir.

c. The odds in favor of the selected student either taking Art or Choir.

7. The Health Science Center Lottery states that players have a 1 in 12 chance of

winning something in their lottery. What are the odds in favor and the odds

against winning this lottery?

8. In roulette, the odds of winning on a single number is 1 : 37. What is the

probability of winning in this game? What is the probability of not winning?

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Assignment #6 Expected Value

1. Sandy pays $5 to play a game. The probability of winning is 60%. She will receive

$10 if she wins.

A) Determine the expected value for this game.

B) Explain whether Sandy should play this game, based on your answer in Part A.

2. A building contractor sets her probability of winning a contract at .30. The

contract is worth $25 000 and she determines it will cost her $2400 to prepare a

contract proposal.

A) Find the expected value of the contract proposal.

B) Is it a good financial decision for her to bid on the contract? Why?

C) What other factors might she consider before deciding whether to bid on the

contract?

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3. Aaron is thinking about adding collision insurance when he renews his car-

insurance policy next year. This will increase the cost of his insurance by $720 per

year.

Statistically, there is a 99.4% chance that Aaron will not have a collision in

the next year.

If Aaron has a collision, the insurance company will pay $5000.

HINT: A “win” for Aaron is an accident (pay out). A “win” for the company is

no accident (no pay out).

A) What is the probability that Aaron will have a collision?

B) What is the expected value for the company if Aaron adds collision

insurance?

C) Should Aaron add collision insurance? Explain.

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4. Dan is buying a clothes dryer that costs $825.

The clothes dryer has a 1 yr warranty from the manufacturer and an

extended 5 yr warranty that cost $50.

The odds against needing repairs over 5 yrs are 3:17.

REMEMBER: A “win” for Dan is needing a repair (pay out). A “win” for the

company is no repair (no pay out).

A) What is the probability that the clothes dryer will need repairs during the

extended – warranty period?

B) What is the probability that the dryer will not need repairs.

C) The company estimates that it costs $200 to repair a dryer. Suppose that

Dan buys the warranty. What is the expected value for the store?

D) Should Dan buy the warranty? Explain. What assumptions did you make?

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