A tennis player makes a successful first serve 51% of the time. if she serves 9 times, what is the probability that she gets exactly 3 first serves in? assume that each serve is independent of the others.

Answer 1

probability is constant and independent of trials.
trials are Bernouli, i.e. either success or failure.
Number of trials is known.
All this point to the binomial distribution where
P(k successes out of n)
=nCk p^k (1-p)^(n-k)
p=probability of success of each independent trial=0.51
n=total number of trials=9
k=3

Answer 2

0.154229089

Answer 3

N=9 p=.51 q=1-.51=.49
9 nCr 3= 84
84(.51^3)(.49^6)
=0.154