Re: help with math problem
More simply put:
The chances you picked the first hat and got two blues is 1/2 x 2/10 x 1/9 or 2/180.
The chances you picked the second hat and got two blues is 1/2 x 8/10 x 7/9 or 56/180.
You are going to get two blues 58 out of 180 times. When you do, there is a 56 out of 58 chance it came from the second hat.
So there is a 56/58 chance that you are looking at an 8/10 probability (to pick a red) and a 2/58 chance you are looking at a 2/10 probability.
56/58 x 8/10 plus 2/58 x 2/10 is 452/580.
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