Waiting for Sixes

Expected Value

Waiting Times

Easy

What is the expected number of rolls of a fair six-sided die until the first

6

appears?

Hint 1

The number of rolls until the first success is geometric.

Hint 2

For Geometric $(p)$ , the mean is $1/ p$ .

Show worked solution

1. Apply the geometric mean formula
The waiting time is Geometric $(1/6)$ , so its expectation is $1/ (1/6) = 6$ .

Answer: 6

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1. Apply the geometric mean formula