Suppose that we have two bags each containing black and white balls. One bag contains 30 white balls and 10 black balls. The other bag contains 30 black balls and 10 white. 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?
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