Compute expected counters after color elimination

Q: Compute expected counters after color elimination

This question evaluates understanding of discrete probability, expected value, and stopping-time concepts in finite sampling without replacement, emphasizing combinatorial reasoning about random draws from a multicolored urn.

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Question

Problem

You have a bag with 30 counters: 10 red, 10 yellow, and 10 blue. You draw counters uniformly at random without replacement. Stop the moment the bag contains counters of only two colors (i.e., right after the 10th counter of some color has been drawn and that color is exhausted).

What is the expected number of counters remaining in the bag at that stopping time?

Assumptions/Clarifications

Draws are without replacement and uniformly random.
The stopping time is the first time any color is exhausted (its 10th counter is drawn). Ties cannot occur because one counter is drawn at a time.

Compute expected counters after color elimination

Problem

Assumptions/Clarifications

Solution

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Compute expected counters after color elimination

Overview

Problem

Assumptions/Clarifications

Solution

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