Mathematical Enigma - XVI
Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year.
Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90 of the time. When it doesn't rain, he incorrectly forecasts rain 10 of the time.
What is the probability that it will rain on the day of Marie's wedding?
Give your answer to 3 decimal places.