Posted by Bersy on Sunday, January 27, 2013 at 3:30pm.
If the probability that a certain tennis player will serve an ace is 1/4, what is the probability that he will serve exactly two aces out of four serves? (Assume that the four serves are independent. Round your answer to four decimal places.)

Math  Damon, Sunday, January 27, 2013 at 4:19pm
I guess I will have to use binomial coefficients.
the probability of k successes in n trials is:
P(k) = C(n,k) p^k (1p)^(nk)
C(n,k) is binomial coef
get from Pascal triangle or table or calculate from
C(n,k)  n! / [ k! (nk)! ]
here
p = prob of ace = .25
(1p) = .75
n = 4
k = 2
C(4,2) = 4! /[2!(2!)] = 4*3*2/[2(2)] = 6
so
P(2) = 6 (.25)^2 (.75)^2
= .21