2001 AMC 12 Problem 11

Question

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?

\dfrac{3}{10}

\dfrac{2}{5}

\dfrac{1}{2}

\dfrac{3}{5}

\dfrac{7}{10}

Answer: D

Concepts:sampling without replacement basic probability symmetry

Difficulty rating: 1530

Small hint:

Imagine drawing all five chips and recording the full order

Big hint:

The drawing ends on the second white exactly when the very last chip in the full order is red

Solution:

Imagine continuing until all five chips are removed. The process actually stops on a white chip exactly when the whites run out before the reds, i.e. when the last chip in the full ordering is red.

The last of the five chips is equally likely to be any chip, so it is red with probability

\dfrac{3}{5}.

Thus, the correct answer is D.