16 Mimi just started her tennis class three weeks ago On ave

16. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent?s serves. Assume her opponent serves 8 times. Show all work. Just the answer, without supporting , will receive no credit. (a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (5 pts) (b) Find the probability that that she returns at least I of the 8 serves from her opponent. (10 pts) (c) how many serves can she expect to return? (5 pts)

Solution

X the number of returns that Mimi gets is binomial.

the events are independent and each trial has success chance p = 0.20

No of trials =8

Prob of failure q = 1-p = 0.80

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b) Probability that she returns atleast 1 of the 8 serves

= P(X>=1)

= 1-P(X=0) = 1-(0.8)⁸

^{= 0.8322}

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c) Expected no of serves = Mean of binomial distribution = np

= 8x0.2 = 1.6

As 1.6 is a decimal we say that out of 40 serves on an average she returns 8 serves.