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 permitted}

Assume:

P(A) = .3

P(B|A) = .75

P(B|A') = .20

P(C|AnB) = .20

P(C|A'nB) = .15

P(C|AnB') = .80

P(C|A'nB') = .90

find P(AUBUC),P(B'nC),P(C').

Find probability that lake contains a poluutant,given that fishing is allowed and the sample tested did not contain a poluutant