Question

On average, your instructor made just 55% of his free throws in high school.

a. what's the probability he makes four out of five?

Answer 1

Assuming constant probability of p=0.55, we can use the binomial distribution, with n=5, x=4 and p=0.55,
P(X=x)=C(n,x)*p^4*(1-p)^(n-x)
=>
P(X=4)=C(5,4) (0.55)^4 (0.45)^1
=5!/(4!1!)(0.55^4) (0.45^1)
=0.2059 (approx.)