(Chung9 ) In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, i.

(Chung9 ) In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, i.e., the probability that it rains, given that she has predicted rain, and the probability that it does not rain, given that she has predicted that it won’t rain, are both equal to 2/3. When rain is forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3. Find the probability that Pickwick has no umbrella, given that it rains.