Question

6 pts Question 13 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. 0.133 0.154 0.00184 0.0635 8 pts

Answer 1

Given :

Probability of success = p = 51% = 0.51

Number of sample = n = 9

Let X be the number of tennis player makes a successful first serve in.

X ~ Binomial (n=9, p=0.51)

The probability density function of Binomial distribution is given by

P(X=x) = (nCx) * p^x * (1-p)^n-x

P(X=3) = (9C3) * (0.51)^3 * (1-0.51)^9-3

= (9C3) * (0.51)^3 (0.49)^6

= 0.154

P(X=3) = 0.154

Therefore probability that she gets exactly 3 first serves in is 0.154

Answer - option b