[kevin017]

this is definitely doable with high school math. i've never heard of bayes theorem, and i just did probably the most convulted and horrible process of solving it, but i came up with 77.9%, or 113/145.

Ok, i just read your above post, i will include what it is that I did. this may be horrible, but here it is.

The odds of drawing two blue marbles from hat 1 are 2/10, then 1/9, or multiply them together to get 2.2%.

The odds of drawing two blue marbles from hat 2 are 8/10, then 7/9, or multiply them together to get 62.2%.

So, we want to set this to 100%. so we add them together, and get 64.4 (62.2 + 2.2), then we divide. 2.2/64.4 = 3.4, and 62.2 / 64.4 = 96.6.

So, the odds of us having gotten the first two blue marbles from hat a is 3.4%, and the odds of us having gotten them from hat b is 96.6%.

So if the first hat was A, the second is B, and the odds of drawing a red marble from b is 2/10. 3.4% * 20% = .68%

If the first hat was B, the second is A, and the odds of drawing a red marble from A is 8/10. 96.6% * 80% = 77.28%

77.28% + .68% = 77.96%