Question

At a Superfund site, 65% of wells are contaminated with volatile organic compounds (VOCs).

The presence of VOCs can be tested using an inexpensive field method to show whether or not VOCs are present or using a more expensive laboratory method to measure the concentration of VOCs. Comparison of field and laboratory analyses has shown that the field tests give a positive result for VOCs 90% of the time that VOCs are really in the water. The field test also gives a positive result for VOCs when VOCs are not in the water 7% of the time. If a sample has tested positive for VOCs using the field method, what is the probability that the sample actually contains VOCs?

Answer 1

Let C represent the event that wells are contaminated with volatile organic compounds (VOCs)

Let P represent the event that the field test gives a positive result.

Then we are given:

P(C) = 0.65

P(C') = 1 - P(C) = 1 - 0.65 = 0.35

P(P/C) = 0.90

P(P/C') = 0.07

We need to find the probability P(C/P)

We will be using Baye's theorem to answer the same.

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