Question

A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 64% chance that the player will miss both shots, a 11% chance that he will make one of the shots, and a 25% chance that he will make both shots. a. Construct the appropriate probability distribution. (Round your answers to 2 decimal places.) b. What is the probability that he makes no more than one of the shots? (Round your answer to 2 decimal places.)

Answer 1

Answer:

a)

$P(X = 0) = 0.64$

$P(X = 1) = 0.11$

$P(X = 2) = 0.25$

b) 0.75 = 75% probability that he makes no more than one of the shots

Step-by-step explanation:

We have these following probabilities:

64% = 0.64 probability that he misses both shots, that is, makes none of them.

11% = 0.11 probability that he makes one shot.

25% = 0.25 probability that he makes both shots.

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

Binomial probability distribution, in which P(X = x) is the probability of making x shots. So

$P(X = 0) = 0.64$

$P(X = 1) = 0.11$

$P(X = 2) = 0.25$

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

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.64 + 0.11 = 0.75$

0.75 = 75% probability that he makes no more than one of the shots