1. Ralph is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 20 days out of 365 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 75% of the time. When it doesn't rain, he incorrectly forecasts rain 25% of the time. What is the probability of rain in a year?
2. Using Bayes' Theorem, what is the probability that it will rain on the day of Ralph's wedding?