Question: Doug has defined the event "It will rain" like this: Today, it will either rain or it will not, but not both. He calls the weather service and they say that it will rain today with probability 0.6, which Doug, for the moment, accepts. Doug knows that Cathy is extremely inaccurate about predicting the weather. He believes that if it is not going to rain on a given day, Cathy will say so with a probability of only 0.1. Similarly, if it is going to rain, he feels Cathy will say so with probability 0.2.
a. Assuming that today it will either rain or it will not (but not both), construct the probability tree for Doug's state of belief.
b. Cathy confidently proclaims, "It's not going to rain today." Given Cathy's statement, what probability does Doug assign that it will rain today?