SOLUTION: 9. Suppose that we have two bags each containing black and white balls. One bag contains 12 white balls and 4 black balls. The other bag contains 4 black balls and 12 white balls.
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Question 1011688: 9. Suppose that we have two bags each containing black and white balls. One bag contains 12 white balls and 4 black balls. The other bag contains 4 black balls and 12 white balls. Suppose we choose one of these bags at random. For this bag we select five balls at random, replacing each ball after it has been selected. The result is that we find 4 white balls and one black. What is the probability that we were using the bag with mainly white balls? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! The second bag has to have 4 white balls and 12 black balls, otherwise the two bags are the same.
mainly white balls
(12/16)(11/15)(10/14)(9/13)(4/12)*5 different ways (another is (4/16)(12/15)(11/14)(10/13)(9/12)
Probability is 0.09066.
Other bag is (4/16)(3/15)(2/14)(1/13)*1, and this is 5 different ways.
Probability is 0.00055
Total is 0.09121
99.4% of it came from the first bag.
99.4%
