2014 AIME I Problems/Problem 2
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Problem 2
An urn contains green balls and blue balls. A second urn contains green balls and blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is . Find .
Solution
First, we find the probability both are green, then the probability both are blue, and add the two probabilities. The sum should be equal to .
The probability both are green is , and the probability both are blue is , so Solving this equation, Multiplying both sides by , we get
See also
2014 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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