Question

5. 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) = 0.20,P(B | A′) = 0.12,P(C |A′ ∩B)=0.14,P(C | A′ ∩ B′) = 0.98.

P(B | A) = 0.85,
P(C | A ∩ B) = 0.06,P(C |A∩B′)=0.80

(a) Find P(B′ | A).

(b) Find P(A ∩ B′ ∩ C).

(c) Find P(B′ ∩ C). Do not round. Hint: Use the Law of Total Probability.

(d) Find the probability that the river is polluted, given that fishing is permitted and

the sample tested did not detect pollution, i.e. find P(A | C ∩ B′).

(e) Find the probability that the sample of water tested does not detect pollution and

fishing is permitted, given that the river is polluted, i.e. find P(B′ ∩ C | A).

Answer 1

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