Question

Chapter P, Section 1, Exercise 037

During the 2015-16 NBA season, Jodie Meeks of the Detroit Pistons had a free throw shooting percentage of 0.906 . Assume that the probability Jodie Meeks makes any given free throw is fixed at 0.906 , and that free throws are independent. Let S denote Successfully making a free throw and F denotes missing it.

( Round ALL your answers to four decimal places. )

(a) If Jodie Meeks shoots TWO free throws in a game, what is the probability that he makes BOTH of them?

P(Makes two) ______

(b) If Jodie Meeks shoots TWO free throws, what is the probability that he misses both of them?

P(Misses two) ____________

(c) If Jodie Meeks shoots TWO free throws, what is the probability that he makes exactly one of them?

P(Makes exactly one) ________________

Answer 1

P[ Jodie Meeks makes any given free throw ] = 0.906

P[ Jodie Meeks does not make any given free throw ] = 1 - Jodie Meeks makes any given free throw

P[ Jodie Meeks does not make any given free throw ] = 1 - 0.906

P[ Jodie Meeks does not make any given free throw ] = 0.094

(a) If Jodie Meeks shoots TWO free throws in a game, what is the probability that he makes BOTH of them?

P[ he makes BOTH of them ] = P[ Jodie Meeks makes any given free throw ]*P[ Jodie Meeks makes any given free throw ]

P[ he makes BOTH of them ] = 0.906*0.906

P[ he makes BOTH of them ] = 0.8208

(b) If Jodie Meeks shoots TWO free throws, what is the probability that he misses both of them?

P[ he misses both of them ] = P[ Jodie Meeks does not make any given free throw ]*P[ Jodie Meeks does not make any given free throw ]

P[ he misses both of them ] = 0.094*0.094

P[ he misses both of them ] = 0.0088

(c) If Jodie Meeks shoots TWO free throws, what is the probability that he makes exactly one of them?

P[ he makes exactly one of them ] = P[ Jodie Meeks makes any given free throw ]*P[ Jodie Meeks does not make any given free throw ] + P[ Jodie Meeks does not make any given free throw ] *P[ Jodie Meeks makes any given free throw ]

P[ he makes exactly one of them ] = 0.906*0.094 + 0.094*0.906

P[ he makes exactly one of them ] = 0.1703