In basketball, a player who is fouled in the act of shooting gets to shoot two free throws.
Suppose we hear that one player is an "85% free throw shooter." If this player is fouled 25 times in the act of shooting (maybe over a period of several games), find the distribution of occasions where he makes both free throws.
That is, if X is the number of times he makes both free throws, find P(X = k) for each k from 0 to 25. How likely is it that he will make both free throws on at least 20 of the 25 occasions?