An NBA player makes...

Question

An NBA player makes a successful free-throw 84% of the time. If he takes 7 shots, find the
probability that he will make:

 

 

a. exactly 5 shots 

 

 

b. at least 6 shots

Answer 1

Both of these questions can be answered with the Binomial Probability formula:

 

nCr * p^r * q^(n-r)  

 

p is the probability of success (meaning the player makes a given free throw)

q is the probability of failure  (meaning the player misses a given free throw)

n is the number of free throws attempted

r is the number of free throws made

 

So for problem a, the probability of making exactly 5 shots out of 7 is:

 

P = 7C5 * (.84)^5 * (.16)^2 = .22483

 

And for problem b, the probability of making at least 6 shots is the probability of making exactly six PLUS the probability of making exactly 7:

 

P = 7C6 * (.84)^6 * (.16)^1 + 7C7 * (.84)^7 * (.16)^0 = .39345 + .29509 = .68854