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
.