Mimi just started her tennis class three weeks ago On averag

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 10 times. (show all work)

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?

b. Find the probability that that she returns at least 1 of the 10 serves from her opponent.

Solution

a)we know that she is able to return 20% of her opponent’s serves, so that\'s her ability to succeed, the rest is its failure

the number of trials (n) = 10

probability of successes (p)= 0.2

and probability of failures (q)= 0.8=(1-p)

b) it ask us that she returns at least 1 of the 10 serves from her opponent.so the probability that should be drawn is not no ball return

f(x)= (10CX)*((0.2)^x)*((0.8)^(10-x)) and x=0,1,2,3,4,5,6,7,8,9,10 we want to know the probability from 1 to 10

F(0)= (10C0)*((0.2)^0)*((0.8)^(10-0)= 0.107374

Now with that probability que can do this = 1-F(x) =1-0.107374 =0.892626

that probability is the probability that that she returns at least 1 of the 10 serves from her opponent.