Problem:
A box contains red chips and green chips. Chips are drawn randomly, one at a time without replacement, until all of the reds are drawn or until both green chips are drawn. What is the probability that the reds are drawn?
Answer Choices:
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Solution:
Consider drawing all five chips and listing the possible outcomes: , , , , , , , , , .
All of these outcomes are equally likely. The outcomes that end in correspond to the outcomes where the reds are drawn and the outcomes that end in correspond to the outcomes where the greens are drawn. The probability that the reds are drawn is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions