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

(a) 4163561

(b) 4161563

(c) 6161563

(d) 163561

(e)161563

Short Answer

Expert verified

The probability that a 6occurs on exactly one of the rolls is option (c) 4161563.

Step by step solution

01

Given information

We roll a fair die four times.

Find the probability that a 6occurs on exactly one of the rolls.

02

Explanation

The probability of 6is 1/6because all die rolls are independent

Then it follows the sampling distribution (4,1/6)

The probability formula is because of the binomial probability density.

X~binomial(4,1/6)

P(X=1)=41161563=4161563

The factorial component is

41=4!1!*(4-1)!=4

So the answer is (c).

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