In: Statistics and Probability
Suppose that we have two bags each containing black and white balls. One bag contains two times as many white balls as black balls. The other bag contains two times as many black balls as 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 all balls are white balls. What is the probability that we were using the bag with mainly black balls?