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) = 0.3. P (B|A) = 0.75, P(P|A') = 0.20, P(C|A∩B) = 0.20, P(C\A'∩P) = 0.15, P(C\A∩B') = 0.80, and P(C|A' n 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.

Transcribed Image Text:

Stion A B C Problems with electricity supplied Computer malfunction Malfunctioning electrical equipment 5 4 2 Caused by other human errors