Ch. 4 Q 1

A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 36% chance that the player will miss both shots, a 14% chance that he will make one of the shots, and a 50% chance that he will make both shots.

a.

Construct the appropriate probability distribution. (Round your answers to 2 decimal places.)

x P(X = x)

0

1 2

b.

What is the probability that he makes no more than one of the shots? (Round your answer to 2 decimal places.)

P( no more than one shot) = P(X=0)+P(X=1) = 0.36+0.14 = 0.50

Probability

c.

What is the probability that he makes at least one of the shots? (Round your answer to 2 decimal places.)

P( atleast one ) = 1 – P( no shot) = 1 – P(X=0) = 1 – 0.36 = 0.64

Probability

Ch. 4 Q 2

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.

Grade Numerical Score

Probability

A

4

0.110

B

3

0.290

C

2

0.370

D

1

0.135

F

0

0.095

Part (a) omitted

b.

Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

Grade P(X ≤ x)

F

D C B A

c.

What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

P( atleast B) = P(A) + P(B) = 0.110 + 0.290 = 0.40

Probability

d.

What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the score = 1 – Failing the score = 1-P(F) = 1 - 0.095 = 0.905

Probability

Ch. 4 Q 3

(Use computer) A committee of 51 members consists of 34 men and 17 women. A subcommittee consisting of 12 randomly selected members will be formed.

a.

What are the expected number of men and women in the subcommittee?

Expected number of Men = np = 12 * 34/51 = 8 & Women = 12 * 17/51 = 4