1. (10 points) Ms. Loveland has a childhood dream to get married at an outdoor ceremony on a rainy day in Tuscon, Arizona. In recent years, it has rained only 10 days each year. The weatherman has predicted rain for tomorrow and thus Ms. Loveland has arranged her wedding ceremony tomorrow. Note that the weatherman correctly forecasts rain 90% of the time. Consider the following 4 events, 0 Event W: rain on a day, 0 Event NW: no rain on a day, 0 Event R : predicting rain on a day, 0 Event N R : predicting no rain on a day, and nd (a) (5 points) Find the probability that the Weatherman predicts rain for a given day, i.e, P[R]. (b) ( 5 points) Find the probability that it will rain tomorrow on MS. Love- land's wedding, i.e. P[W|R]