Abasketball 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?

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) = 

where n=11, x=5
Therefore,
P(X=5) =   = 0.2255

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