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

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.

2001 AMC 10 Problem 23

Answer: D

Difficulty rating: 1690

Solution:

Problem 23 in Other Years