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Chapter 7: Q.7.22 (page 354)

How many times would you expect to roll a fair die before all 6sides appeared at least once?

Short Answer

Expert verified

The expected number is14.7

Step by step solution

01

Given Information

we have that random variable Ij∈ℕ0has Geometric distribution with the parameter of success 6-j+16. The total number of needed throws is N=∑jIj.

02

Explanation

Therefore, the expected number is,

E(N)=∑jE(Ij)=∑j16−j+16=∑j66−j+1=14.7

03

Final Answer

The expected number is14.7

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