1 A tennis player makes a successful first serve 59 of the t

1. A tennis player makes a successful first serve 59% of the time. If she serves 7 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others

2.

In a small class of 5 students, there is a probability of 0.80 that a student will ask a question at the start of class. Assuming that students decide to ask a question independently of each other, what\'s the probability that there will be at least one question at the start of class?

Select one:

a. (0.2)^5 (0.2 raised to the 5th power)

b. 1 - (0.8)^5 (1 minus 0.8 raised to the 5th power)

c. 1- (0.2)^5 (1 minus 0.2 raised to the 5th power)

d. (0.8)^5 (0.8 raised to the 5th power)

Solution

A tennis player makes a successful first serve 59% of the time. If she serves 7 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others

It follows binomial distribution with parameter

p=59%=0.59,

q=1-p=1-0.59=0.41

n=7

and r=3

we know P(X=r)=nCr*(p)^r *(q)^(n-r) So, P(X=r)=7C3*(0.59)^3*(0.41)^4=0.203(Ans.

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d. (0.8)^5 (0.8 raised to the 5th power)