Question

A certain tennis player makes a successful first serve 61​% of the time. Assume that each serve is independent of the others. If she serves 5 ​times, what's the probability she gets​ a) all 5 serves​ in? b) exactly 3 serves​ in? c) at least 3 serves​ in? d) no more than 3 serves​ in?

Answer 1

X: number of serves in.

X ~ bin(n,p)

where, n= 5

p =61% = 0.61

q= (1-p)= (1-0.61) = 0.39

the pmf of the distribution be:-

a). the probability that she gets all 5 serves in be:-

= 0.0845

b)the probability that she gets all 5 serves in be:-

= 0.3452

c).the probability that she gets at least 3 serves in be:-

= 0.6997

d).the probability that she gets no more than 3 serves in be:-

= 0.6455

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