In Edinburgh, % of the days have some rain. The weather forecaster is correct 3 of the time, i.e., the probability that it rains, given that she has predicted rain the day before, and the probability that it does not rain given that she has predicted that it won't rain the day before, are both equal to 3. When rain is forecast, Mr. Coppereld takes his umbrella. When rain is not forecast, he takes it With probability % (a) What is the probability that the forecaster predicts rain today? [2 marks] (b) On any given day, What is the probability that Mr. Coppereld takes his umbrella? [2 marks] (0) It was raining today. What is the probability that the forecaster predicted this? [2 marks]