Question

A certain tennis player makes a successful first serve 64​% of the time. Assume that each serve is independent of the others. If she serves 9 ​times, what's the probability she gets​

a) all 9 serves​ in?
b) exactly 6 serves​ in?
c) at least 7 serves​ in?
d) no more than 6 serves​ in?

Answer 1

0.0181,0.2693,0.1092,0.4163

Explanation:

Given that a certain tennis player makes a successful first serve 64​% of the time.

Since each serve is independent of the other

X the no of serves in is Binomial with n = no of times he serves =9

and p = constant probability = 0.64

X is Bin (9,0.64)

Probability that she get in

a) all 9 serves​ in?

=
`P(X=9) = 0.64^9\\=0.0181`

b) exactly 6 serves​ in?

P(x=6)

=
`9C6 (0.64)^6 (1-0.64)^3\\=0.2693`

c) at least 7 serves​ in

=
`P(X\geq 7) = 0.1092`

d) no more than 6 serves​ in

=
`P(X<6)= 0.4163`