Question

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.

There is already an explanation/walkthrough for this problem on Chegg but it doesn't explain WHY he used the formulas that he uses. I can plug numbers into a formula but I'm not sure which ones to use because there are many ways to arrange the given information. So my question is which formulas do you use and the concept behind why you chose that formula?

Answer 1

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