2014 AIME I Problems/Problem 2
An urn contains green balls and
blue balls. A second urn contains
green bals 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 1:The probability of drawing balls of the same color is the sum of the probabilities of drawing two green balls and of drawing two blue balls. This give us