Problem:
A red ball and a green ball are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin is for What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?
Answer Choices:
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B.
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E.
Solution:
The probability that the two balls are tossed into the same bin is
Therefore the probability that the balls are tossed into different bins is . By symmetry the probability that the red ball is tossed into a higher-numbered bin than the green ball is .
The problems on this page are the property of the MAA's American Mathematics Competitions