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2001 AMC 10 Problem 23

Problem 23 of 25HarderCounting & Probability

A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white?

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Solution

Imagine drawing all five chips in a random order. The drawing stops on a white chip exactly when both white chips come out before all three reds, which happens precisely when the very last chip in the full ordering is red. That probability is 35.\dfrac{3}{5}. Thus, the correct answer is D.

More practice

Concepts: sampling without replacement · basic probability · symmetry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.