A certain tennis player makes a successful serve 64% of the time. Assume that each serve is independant of the others. If she serves 9 times, what is the probability she a) serves all 9 in? b)serves exactly 8 in?c) serves at least 7 in? d) serves no more than 7 in?

Question

campbell_st · Answer

well its binomial probability 

p = 0.64     serve success
q = 0.36      serve failure

so the probability of k successes from n trials is 

$$P(k ..successes.. from ..9 ..trials) = ^9C_{k} (0.64)^{k}(0.36)^{9 - k}$$

so for the 1st question k = 9

2nd k = 8

3rd, at least 7  is k = 7 + k = 8 + k = 9

4th    1 - (k = 8 + k = 9)

hope this helps