Problem 1 [10 points]. Marie is getting married tomorrow at an outdoor ceremony in NYC. In recent years, t rained about once every three days. The weatherman has predicted there w be no rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 80% of the time. When it doesn't rain, he incorrectly forecasts rain 20% of the time. What is the probability that it will rain on the day of Marie's wedding according to Bayes' rule