In Problem 19.12, a vendor at a baseball stadium is deciding whether to sell ice cream or soft drinks at today's game. Prior to making her decision, she decides to listen to the local weather forecast. In the past, when it has been cool, the weather reporter has forecast cool weather 80% of the time. When it has been warm, the weather reporter has forecast warm weather 70% of the time. The local weather forecast is for cool weather.

a. Revise the prior probabilities now that you know that the weather forecast is for cool weather.

b. Use these revised probabilities to repeat Problem 19.12.

c. Compare the results in (b) to those in Problem 19.12.