In: Statistics and Probability
There are four urns, which we label A, B, C, and D, and each of these urns contains some white balls and some black balls, as specified below.•UrnAhas3white balls and2black balls•UrnBhas2white balls and6black balls•UrnChas3white balls and6black balls•UrnDhas5white balls and7black balls one of the urns is chosen at random, and then one of the balls is selected from the chosen urn.
(a) What is the probability that urnAis chosen, and then a white ball is chosen from thaturn?
(b) What is the overall probability that a white ball is chosen?
(c) If a white ball is chosen, what is the probability that it came from urnA?
(d) If a black ball is chosen, what is the probability that it came from urnA?