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Chapter 6: Q. 114 (page 431)

If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?

a. 0.25

b. 1.00

c. (41)(0.25)3(0.75)341(0.25)3(0.75)3

d. (41)(0.25)1(0.75)341(0.25)1(0.75)3

e.(0.75)3(0.75)1

Short Answer

Expert verified

Option (d) is the correct answer

Step by step solution

01

Given Informaiton

Number of trials (n)=4

Probability of success(p)=14=0.25

02

Simplification

Consider, X is a random variable that depicts the number of games that are won follows the binomial distribution with n=4and p=0.25.

The probability that Jeff will win exactly 1 prize can be calculated as:

P(X=1)=41(0.25)1(1-0.25)4-1=41(0.25)1(1-0.25)3

Thus, the required probability is 41(0.25)1(1-0.25)3.

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