Suppose you wish to determine the television channel on which you should watch the evening news to learn about the next day’s weather. There are two main channels (say 1 and 2) that you can choose from. Your main criterion is the accuracy of the weather forecast, and you believe that the weather forecaster can be either “good” (g) or “bad” (b). Right now, you think that there is a 50-50 chance that the weather forecaster on either channel is good, that is, your (prior) belief is that the probability is 0.5 that the weather forecaster is g on either channel. You also realize that nobody is perfect, so that a good forecaster has a 0.8 chance of being right and a bad forecaster has a 0.5 chance of being right. Imagine for now that the forecasters on both channels give you

“point estimates” (i.e., they will tell you whether or not it will rain tomorrow) rather than probabilistic forecasts (e.g., there is a 60% chance of rain). Suppose that the forecaster on channel 1 said last night that it would rain today and forecaster on channel 2 said that it would not. If you observe rain, how should you revise your beliefs?