Problem:
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?
Answer Choices:
A.
B.
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E.
Solution:
Think of continuing the drawing until all five chips are removed form the box. There are ten possible orderings of the colors: , , , , , , , , , and . The six orderings that end in represent drawings that would have ended when the second white chip was drawn.
Imagine drawing until only one chip remains. If the remaining chip is red, then that draw would have ended when the second white chip was removed. The last chip will be red with probability .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions