Rolls of a d12 until an odd number appears

Question

A fair die with faces $1$ through $12$ is rolled until it shows an odd number. What is the expected number of rolls?

Short answer

$2$ . Six of the twelve faces are odd, so each roll succeeds with probability $\tfrac12$ and the waiting time is geometric with mean $2$ .

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Lessons behind this question

Expectation, Mean, and Variance
Counting and Combinatorics
Conditional Expectation and Variance Revisited

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