My problem is:
My first urn contains 10 balls, 4 red and 6 blue. My second one contains 16 red balls and some blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. How many blue balls are in the second urn.
I tried to muddle through it using P(A) and P(B) type notation, but I got nowhere. My solution is below:
I noticed that my odds of getting the same ball are on a straight line. With the X axis as the percentage of red balls in the second urn, and the Y axis as the percentage of balls being the same color, I got (0, 0.4), (50, 0.5), and (100, 0.6). So I just mentally plotted (20, 0.44). That gives me 20% of the urn 2 total being blue, for 4 balls.
I'm pretty sure this is correct since it's one of my choices, I'm just not sure this is the way it's supposed to be done. Is there a way to do this without even mental graphing? A way that uses P(A), P(A'), etc.?