# MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) (6 points) Which of the following is a valid probability distribution for a sample space S = {a, b, c, d}? A) P(a) = 0.5, P(b) = 0.2, P(c) = 0.1, P(d) = 0.3 B) P(a) = 0.3, P(b) = 0, P(c) = 0.2, P(d) = 0.5 C) P(a) = 0.5, P(b) = 0, P(c) = 0.3, P(d) = 0.1 D) P(a) = -0.2, P(b) = 0.5, P(c) = 0.4, P(d) = 0.3 2) (6 points) Events E and F are independent if A) P(E ? F) = P(E)P(F) B) P(E ? F) = 0 C) P(E ? F) = 0 D) P(E ? F) = P(E) + P(F) 3) (6 points) Two events A and B are mutually exclusive if A) A ? B = U. B) A ? B = U. C) A ? B = . D) A ? B = . 4) (6 points) Suppose that P(E) = 0.85, P(F) = 0.4, and P(E ? F) = 0.35. Calculate P(F|E). A) B) C) D) 5) (6 points) What is the probability that a family with six children has exactly three boys? A) B) C) D) 6) (6 points) The manager of a small retail store counted the number of sales each hour during a 60-hour week. The frequency distribution is given below. Find the relative frequency of eight sales during an hour. A) B) C) D) 7) (6 points) A biased coin with P(H) = 1/4 and P(T) = 3/4 is thrown twice, find the probability of getting two heads. A) B) C) D) The table below gives crime statistics relating to the location of the crime and the type of crime. 8) (6 points) Find the probability that a randomly-selected crime committed in a commercial area was a robbery. A) B) C) D) 9) (6 points) Find the probability that a randomly-selected crime was committed in a residential area given that it was an assault. A) B) C) D) 10) (6 points) Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5. Find P(E ? F). A) 0.8 B) 0.12 C) 1 D) 0.7 SHORT ANSWER. Show your work and calculations for each question. 11) (10 points) A factory produces screws, which are packaged in boxes of 30. Four screws are selected from each box for inspection. A box fails inspection if two or more of these four screws are defective. What is the probability that a box containing two defective screws will pass inspection? 12) (6 points) What are the odds in favor of Brown winning an election if the probability that he will lose is 0.83? 13) (6 points) Let E and F be events such that P(E) = 0.7, P(F) = 0.5, P(E ? F) = 0.4. Find P(E ? F). 14) A certain soccer goalkeeper catches 30% of all penalty kicks against her team. a) (9 points) What is the probability that out of five penalty kicks she catches two? b) (9 points) What is the probability that out of five penalty kicks she catches at least two?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) (6 points) Which of the following is a valid probability distribution for a sample space S = {a, b, c, d}?

A)
P(a) = 0.5, P(b) = 0.2, P(c) = 0.1, P(d) = 0.3

B)
P(a) = 0.3, P(b) = 0, P(c) = 0.2, P(d) = 0.5

C)

P(a) = 0.5, P(b) = 0, P(c) = 0.3, P(d) = 0.1

D)

P(a) = -0.2, P(b) = 0.5, P(c) = 0.4, P(d) = 0.3

2)

(6 points) Events E and F are independent if

A)

P(E ? F) = P(E)P(F)

B)

P(E ? F) = 0

C)

P(E ? F) = 0
D)

P(E ? F) = P(E) + P(F)

3)

(6 points) Two events A and B are mutually exclusive if

A)

A ? B = U.

B)

A ? B = U.

C)

A ? B = .

D)

A ? B = .

4)

(6 points) Suppose that P(E) = 0.85, P(F) = 0.4, and P(E ? F) = 0.35. Calculate P(F|E).

A)

B)

C)

D)

5)

(6 points) What is the probability that a family with six children has exactly three boys?

A)

B)

C)

D)

6)

(6 points) The manager of a small retail store counted the number of sales each hour during a 60-hour week. The frequency distribution is given below.

Find the relative frequency of eight sales during an hour.

A)

B)

C)

D)

7)

(6 points) A biased coin with P(H) = 1/4 and P(T) = 3/4 is thrown twice, find the probability of getting two heads.

A)

B)

C)

D)

The table below gives crime statistics relating to the location of the crime and the type of crime.

8)

(6 points) Find the probability that a randomly-selected crime committed in a commercial area was a robbery.

A)

B)

C)

D)

9)

(6 points) Find the probability that a randomly-selected crime was committed in a residential area given that it was an assault.

A)

B)

C)

D)

10)

(6 points) Let E and F are mutually exclusive and P(E) = 0.2 and P(F) = 0.5.
Find P(E ? F).

A)

0.8

B)

0.12

C)

1

D)

0.7

11)

(10 points) A factory produces screws, which are packaged in boxes of 30. Four screws are selected from each box for inspection. A box fails inspection if two or more of these four screws are defective. What is the probability that a box containing two defective screws will pass inspection?
12) (6 points) What are the odds in favor of Brown winning an election if the probability that he will lose is 0.83?

13) (6 points) Let E and F be events such that P(E) = 0.7, P(F) = 0.5,
P(E ? F) = 0.4. Find P(E ? F).

14) A certain soccer goalkeeper catches 30% of all penalty kicks against her team.
a) (9 points) What is the probability that out of five penalty kicks she catches two?
b) (9 points) What is the probability that out of five penalty kicks she catches at least two?