2014 AIME I Problems/Problem 2

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 0.58. Find .

Solution

First, we find the probability both are blue, then the probability both are green, and add the two probabilities which equals . The probability both are blue is , and the probability both are green is , so Solving this equation, we get .