Wutao bought a ticket to Purdue's next football game at Ross-Ade Stadium. He checked the weather for game day and found that there is 60% chance of rain. Looking back at historical data on Purdue home football games and weather conditions, when it rains, Purdue wins 44% of the time; when it does not rain, Purdue loses 27% of the time.
a) Draw a tree diagram corresponding to the above information.
b) What's the probability that at the next home game Purdue wins in the rain?
c) What is the probability that Purdue loses the next game?
d) If Purdue wins the next game, what is the probability that the weather was rainy?