Module 4 Prelims & Final Quiz

 A cooler has a total of 17 cans of soda in it.   Of the cans in the cooler, 5 are Diet Coke, 3 are regular Coke and the rest are Coke Zero. 

If one can is randomly selected, what is the probability it is a Coke Zero?  

Round your answer to two decimal places.

0.53

If two events, A and B, are NOT disjoint (not mutually exclusive), then P(A or B) = ....

A. P(A) + P(B) + P(A and B)

B. P(A) + P(B) - P(A and B)

C. P(A) + P(B)

D. none of these

B. P(A) + P(B) - P(A and B)

If an adult is randomly selected from a specific city, the probability they are retired is 0.31, the probability they are married is 0.63, and the probability they are retired and married is 0.17.  What is the probability that a randomly selected adult from this city will be married or retired? 

0.77

There are 26 letters in the alphabet.

What is the probability that a randomly selected letter comes before the letter J alphabetically?

A. 8/26

B. 9/26

C. 12/26

D. 11/26

B. 9/26

There are 26 letters in the alphabet.

What is the probability that a randomly selected letter comes before the letter J alphabetically given the letter is in the word "uncopyrightable"?

A. 7/15

B. 9/15

C. 7/9

D. 9/26

E. 7/26

A. 7/15

A sample of 140 non-pet owners were asked why they did not have a pet.  Their answers are summarized in the table below.  If a non-pet owner is randomly selected, what is the probability they do not have a pet because it is too costly or too much responsibility?

Reason for not having a Pet	Frequency	Relative Frequency
Too Costly	54	0.386
Allergic	13	0.093
Too much responsibility	43	0.307
Other	30	0.214
total	140	1

A. 0.60

B. 0.693

C. 0.386

D. 0.307

B. 0.693

A cooler contains 8 sodas, 5 are Coca-Cola and 3 are Pepsi. If a person randomly selects two sodas to drink from the cooler, what is the probability they select two Coca-Colas?

A. 0.391

B. 0.3125

C. 0.357

D. 0.40

C. 0.357

A cooler contains 8 sodas, 5 are Coca-Cola and 3 are Pepsi. If a person randomly selects two sodas to drink from the cooler, what is the probability they select one Coca-Cola and one Pepsi?

A. 0.536

B. 0.234

C. 0.469

D. 0.268

A. 0.536

If event A and event B are independent events then P(A and B) =

A. P(A) + P(B) - P(A and B)

B. P(A) x P(B)

C. P(A) / P(B)

D. P(A) + P(B)

B. P(A) x P(B)

If P(A and B) = P(A) x P(B) then we know that event A and event B are

A. dependent events

B. independent events

C. mutually exclusive events (a.k.a. disjoint events)

D. not mutually exclusive events (a.k.a. not disjoint events)

B. independent events

It is known that 60% of the students at a large university have a job and 40% do not have a job.    If two students are randomly selected, what is the probability neither has a job?

A. 0.16

B. 0.80

C. 0.40

D. 0.20

A. 0.16

It is known that 60% of the students at a large university have a job and 40% do not have a job. If three of these students are randomly selected, what is the probability all three have jobs?

A. 0.216

B. 0.060

C. 0.648

D. 0.360

A. 0.216

It is known that 60% of the students at a large university have a job and 40% do not have a job. If two of these students are randomly selected, what is the probability that one will have a job and one will not have a job?

A. 0.50

B. 0.24

C. 0.48

D. 0.38

C. 0.48

It is known that 60% of the students at a large university have a job and 40% do not have a job.    If two of these students are randomly selected, what is the probability that at least one will have a job? 

A. 0.84

B. 0.48

C. 0.50

D. 0.60

A. 0.84

A and B are events such that P(A) = 0.5 and P(B) = 0.2. For each additional property listed, find the value for the requested probability

___If A and B are independent, find P(A and B)

___If A and B are mutually exclusive, find P(A and B)

1.0.6

2.0.7

3.0.1

4.0

5.0.3

3,4

Events that are mutually exclusive cannot occur at the same time, meaning it is impossible to have both of them occur simultaneously.

Events that are independent can occur at the same time and are their product.

A box has 6 AA batteries in it, however one of the  AA batteries is dead while the rest are good batteries.   If two batteries are randomly selected from the box, what is the probability both are good batteries?

Round your answer to two decimal places.

0.67

A flipped coin will show heads 50% of the time and tails 50% of the time. 

If a coin is flipped three times, what is the probability it lands heads all three times?

Do not round your answer. 

0.125

A standard six-sided die will be rolled twice. What is the probability the number four is rolled both times?

A. 0.333

B. 0.167

C. 0.028

D. 0.067

C. 0.028

P(X) = 0.8, P(Y) = 0.5, and P(X and Y) = 0.4

According to this information, which two of the following are true statements

Select 2 correct answer(s)

A. Events X and Y are disjoint (mutually exclusive)

B. Events X and Y are not disjoint

C. Events X and Y are independent

D. Events X and Y are not independent

B. Events X and Y are not disjoint

C. Events X and Y are independent

Zoey is selling chocolate bars as a fund-raiser. She has 2 chocolate bars with almonds left to sell and 6 chocolate bars with caramel left to sell.  If 2 of Zoey's candy bars are randomly selected, what is the probability both have almonds?

Round your answer to two decimal places.

0.04

It a given region, it is known that 72% of the people have been exposed to a virus. If two people in this region are randomly selected, what is the probability one was exposed to the virus and the other person was not exposed to the virus? 

Round your final answer to THREE decimal places. 

0.403

It is known that 73% of all travelers at an airport are domestic travelers (staying within the  U.S.) while the rest are international travelers.     If three travelers are randomly selected, what is the probability all three are domestic travelers? 

Round your final answer to THREE decimal places. 

0.389

It is given that P(A) = 0.5, P(B) = 0.2, and P(A and B) = 0

Select all true statements about events A and B

A. Events A and B are independent

B. Events A and B are mutually exclusive

C. neither statement above is true

B. Events A and B are mutually exclusive

A child's board game has a spinner has 4 different colors on which the spinner can stop.  The spinner is equally likely to stop on each of the 4 colors.  One color on the spinner is red.  If the spinner is spun 3 times, what is the probability it stops on red all 3 spins? 

Round your answer to THREE decimal places  (e.g. 0.3892849 would round to 0.389)

0.016

There are 26 letters in the alphabet. A letter from the alphabet is randomly selected.

Match the answers to their corresponding probability questions.

___What is the probability that the selected letter is in the word "pencil" or in the word "notable" ?

___What is the probability that the selected letter is in the word "pencil" and in the word "notable" ?

1.3/26

2.3/13

3.10/26

4.13/26

3,1

There are 26 letters in the alphabet. If one letter is randomly selected, what is the probability that the selected letter is in the word "pencil" given it is in the word "notable" ?

A. 3/6

B. 6/7

C. 3/13

D. 6/10

E. 3/7

E. 3/7

The results of a study on 150 people's eating habits provided the following data. Each person self selected the category that fit them best.  If a person is randomly selected, what is the probability they are Vegan or Gluten Free?

Dietary Restrictions	Frequency
Vegan	9
Vegetarian	22
No restrictions	89
Gluten Free	30
total	150

A. 0.2

B. 0.26

C. 0.06

D. 0.147

B. 0.26

The results of a study on 150 people's eating habits provided the following data. Each person self selected the category that fit them best.  If a person is randomly selected, what is the probability they are Vegetarian given they are not Gluten Free?

Dietary Restrictions	Frequency
Vegan	9
Vegetarian	22
No restrictions	89
Gluten Free	30
total	150

A. 0.183

B. 0.347

C. 0

D. 0.147