A fishing magazine collected data and printed the following results:

If there is rain then the probability of catching a fish at Lake Blue is 80%, but if it doesn't rain then the probability of catching a fish at Lake Blue is 17%. The forecast for today is 68% chance of rain.

a) What is the probability that it rained today and a fish was caught?

b) What is the probability of catching a fish today?
P(R not R|R) = 0.20 x 0.68 = 0.136

c) If a person caught a fish, what is the probability that there was rain?