Red apples left when the last green is drawn

Question

A basket holds $4$ green apples and $50$ red apples. Apples are taken out one at a time at random, without replacement, and the process stops as soon as the fourth green apple has been removed. On average, how many apples remain in the basket at that point?

Short answer

$10$ . The four green apples cut the random ordering of the $50$ red ones into five gaps, which by symmetry have equal expected size $50/5=10$ . The apples remaining are exactly the gap after the last green.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free