Question 1

A single card is drawn from a standard 52-card deck. Find the probability of each of the following events. Give your answers as reduced fractions.

a) The card drawn is a face card (i.e. a Jack, Queen or King). P(face card) =

b) The card drawn is not a face card. P(not a face card) =

c) The card drawn is a heart.

P(heart) =

d) The card drawn is a face card and a heart.

P(heart and face card) =

e) The card drawn is a face card or a heart. P(face card or heart) =

Question 2

A single card is drawn from a standard 52-card deck. Find the probability of each of the following events. Give your answers as reduced fractions.

a) The card drawn is a 9. P(9) =

b) The card drawn is not a 9. P(not a 9) =

c) The card drawn is a heart. P(heart) =

d) The card drawn is a 9 and a heart. P(heart and 9) =

e) The card drawn is a 9 or a heart. P(heart or 9) =

Question 3

Let A, B be events with P(A) = .45, P(B) = .60, and P(A and B) = .25.

Find P(B|A)

Group of answer choices

a. 0.417

b. 0.556

c. 0.27

d. 0.80

Question 4

Let A,B be events with P(A)=0.20,P(B)=0.50,and P(B|A)=0.3.

Find P(A and B)

Group of answer choices

a. 0.10

b. 0.06

c. 0.12

d. 0.70

Question 5

Suppose that A, B are two independent events, with P(A) = 0.8 and P(B) = 0.4.

Calculate the following probabilities for parts a through d, and give your answer as a decimal rounded to two decimal places. Answer part e as either "yes" or "no":

a) P(not B) = b) P(A and B) = c) P(A or B) = d) P(B | A) = e) Are events A and B mutually exclusive?

Question 6

Suppose that A, B are two independent events, with P(A) = 0.5 and P(B) = 0.4.

Calculate the following probabilities for parts a through d, and give your answer as a decimal rounded to two decimal places. Answer part e as either "yes" or "no":

a) P(not B) = b) P(A and B) = c) P(A or B) = d) P(B | A) = e) Are events A and B mutually exclusive?

Question 7

A jar contains 8 red balls, 7 white balls, and 4 yellow balls. Two balls are drawn randomly from the jar without replacement.

Find the probability of the given event, and write your answers as fractions.

a) The second ball is red, given that the first ball is yellow: P(red | yellow) =

b) The second ball is yellow, given that the first ball is red: P(yellow | red) =

c) Both balls are red: P(both are red) =

Question 8

A jar contains 7 red balls, 5 white balls, and 9 yellow balls. Two balls are drawn randomly from the jar without replacement.

Find the probability of the given event, and write your answers as fractions.

a) The second ball is white, given that the first ball is yellow: P(white | yellow) =

b) The second ball is yellow, given that the first ball is white: P(yellow | white) =

c) Both balls are yellow: P(both are yellow) =

Question 9

The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 Total: 9313 What is the probability that a randomly selected degree is in Engineering?

Group of answer choices

a. 0.0012

b. 0.1028

c. 0.0932

d. 868

Question 10

A class consists of 13 women and 29 men. If a student is randomly selected, what is the probability that the student is a woman?

Group of answer choices

a. 13/42

b. 1/42

c. 29/42

d. 13/29

Question 11

When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 10?

Group of answer choices

a. 1/60

b. 2/9

c. 4/9

d. 4/3

Question 12

A study of consumer smoking habits includes 155 people in the 18-22 age bracket (42 of whom smoke), 131 people in the 23-30 age bracket (34 of whom smoke), and 85 people in the 31-40 age bracket (28 of whom smoke).

If one person is randomly selected from this sample, find the probability of getting someone who is age 18-22 or does not smoke.

Group of answer choices

a. 0.305

b. 0.729

c. 1.137

d. 0.833

Question 13

If a single fair die is rolled, find the probability that the number rolled is 5 given that it is odd.

Group of answer choices

a. 2/3

b. 1.3

c. 1/2

d. 1/6

Question 14

If two fair dice are rolled, find the probability that the sum is 6 given that the roll is a "double".

Group of answer choices

a. 1/6

b. 1/3

c. 1/5

d. 1/4

Question 15

In a large town, 73% of adults have health insurance. What is the probability that 9 randomly selected adults from the town all have health insurance?

Group of answer choices

a. 0.73

b. 0.059

c. 0.123

d. 6.57

Question 16

A family has five children. The probability of having a girl is 1/2. What is the probability of having 3 girls followed by 2 boys?

Group of answer choices

a. 5/16

b. 1/16

c .1/32

d. 1/120

Question 17

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards.

Find the probability that the first card is a king and the second card is a queen.

Group of answer choices

a. 2/13

b. 1/169

c. 1/13

d. 4/663

Question 18

Three cards are drawn in order from a well shuffled deck of 52 cards.

The probability that all three cards are clubs is given by:

Group of answer choices

a. (13/52)x (12/52)x (11/52)

b. (13/52) x (13/52) x (13/52)

c. (13/52) x (13/51)x (13/50)

d. (13/52) x (12/51) x (11/50)

Question 19

The table below shows the soft drinks preferences of people in three age groups.