Question

A basketball player has a 50% chance of making each free throw. what is the probability that the player makes exactly five out of eleven free throws?

Answer 1

Free throw follows binomial distribution.
probability of making free throw = probability of success = 0.5 = p
probability of fail = 1-0.5 = 0.5 = q

Binomial distribution is given by,
P(X) =
`^nC_(x) p^(x) q^(n-x)`

where n=11, x=5
Therefore,
P(X=5) =
`^(11)C_(5) (0.5)^(5) (0.5)^(11-5)` = 0.2255