2001 AMC 10 Problem 23

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}

\dfrac25

\dfrac12

\dfrac35

\dfrac{7}{10}

Answer: D

Concepts:sampling without replacement basic probability symmetry

Difficulty rating: 1690

Small hint:

Imagine drawing all five chips; the game stops when one color is exhausted

Big hint:

The last drawn chip is white exactly when the very last of all five chips is red

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

\dfrac{3}{5}.

Thus, the correct answer is D.