Emptying the bowl when red cherries run out

Question

A bowl holds $5$ red and $8$ purple cherries. Amy removes cherries one by one at random and stops as soon as no red cherries remain. What is the probability that she has emptied the bowl at that point?

Short answer

$5/13$ . She empties the bowl exactly when the very last cherry in the random order is red. Each of the $13$ cherries is equally likely to be last, and $5$ are red.

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Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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