Show all work to arrive at final answer thanks Consider a ba

Show all work to arrive at final answer. thanks

Consider a basketball player with an 85% free-throw percentage. What is the probability of making 18 free throws before missing one? Before missing two?

Solution

a)

Here, this is a negative binomial distribution.

P(k, r) = C(k + r- 1,k) p^k (1- p)^r

Thus, for k = 18 successes before r = 1 failure,

P(18,1) = 0.008046961 [answer]

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b)

Here, this is a negative binomial distribution.

P(k, r) = C(k + r- 1,k) p^k (1- p)^r

Thus, for k = 18 successes before r = 2 failures,

P(18,2) = 0.02293384 [answer]