All even faces before any odd face

Question

A fair die is rolled repeatedly until each of its six faces has turned up at least once. What is the probability that the three even faces all appear before the first odd face shows up?

Short answer

$1/20$ . Only the order in which faces first appear matters, and all $6!$ such orders are equally likely. The favourable ones put the three evens first in any order and then the three odds, giving $\tfrac{3!\,3!}{6!}=\tfrac1{20}$ .

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Counting and Combinatorics
Expectation, Mean, and Variance

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