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|ac ) = 0.2, p c|a∩b = 0.2, p c|ac∩b = 0.15, p c|a∩bc = 0.8 and p c|ac ∩ bc = 0.9, then find (1) p(a ∩ b ∩ c) (2) p(bc ∩ c) (3) p(c) (4) find the probability that the river is polluted, given that fishing is permitted and the sample tested did not detect pollution. hint: de-morgan’s law (a ∩ b) c = ac ∪ b