Pollution of the rivers in the United States has been a problem for many years. Consider the following events: A: the river is polluted, B: a sample of water tested detects pollution, C: fishing is permitted. Assume P(A) = 0.3, P(B|A) = 0.75, P(B|A') = 0.20, P(C|A∩B) = 0.20, P(C|A'∩B) = 0.15, P(C|A∩B') = 0.80, and P(C|A'∩B') = 0 .90. 

(a) Find P(A∩B∩C).  

(b) Find P(B'∩C). 

(c) Find P(C). 

(d) Find the probability that the river is polluted, given that fishing is permitted and the sample tested did not detect pollution.