Tree diagrams can organize problems having more than two stages. The figure shows probabilities for a charity calling potential donors by telephone. Each person called is either a recent donor, a past donor, or a new prospect. At the next stage, the person called either does or does not pledge to contribute, with conditional probabilities that depend on the donor class to which the person belongs. Finally, those who make a pledge either do or don’t actually make a contribution. Suppose we randomly select a person who is called by the charity.

a. What is the probability that the person contributed to the charity?

b. Given that the person contributed, find the probability that he or she is a recent donor.

0.8 Contribute 0.4 Pledge Recent 0.2 donor Not 0.6 No pledge 0.5 0.6 Contribute 0.3 Pledge 0.3 Past 0.4 Not donor No pledge 0.7 0.2 0.5 Contribute 0.1 Pledge New 0.5 Not prospect 0.9 No pledge