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Chapter 7: Q. 2.5 (page 438)

Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?

a.4(16)3(56)14163561b.(16)3(56)1163561c.4(16)1(56)3161563d.(16)1(56)3161563e.6(16)1(56)36161563

Short Answer

Expert verified

The probability that a 6 occurs on exactly one of the rolls is4(16)1(56)3161563.

Step by step solution

01

Given Information

Let roll four times with a fair die

Formula used:

P(X=r)=C1n(p)r(q)n-r

02

Explanation for correct option

Because each die roll is unique,

X~binomial(4,1/6)

P(X=1)=C14161563

=4脳16脳563

Therefore, the correct option is (c)

03

Explanation for incorrect option

(a) The probability that a 6 occurs on exactly one of the rolls is not 4(16)3(56)14163561

(b) The probability that a 6 occurs on exactly one of the rolls is not (16)3(56)1163561

(d) The probability that a 6 occurs on exactly one of the rolls is not (16)1(56)3161563

(e) The probability that a 6 occurs on exactly one of the rolls is not 6(16)1(56)36161563

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