It has been observed over the past several decades that the probability of the n

Question

It has been observed over the past several decades that the probability of the natural gas reserve is present in certain regions in the US is 0.7.

A seismic survey can be used to further help in our decision making process by predicting the presence of the gas. Historically, seismic survey was 83% of the time correct when gas was indeed present and 93% of the time correct when gas was not present.

Calculate the probability that the gas is indeed present if the seismic survey says it is not present.

Explanation / Answer

P(survey says no) = P(gas but survey wrong OR no gas but survey right) = (0.7)(0.12) + (0.3)(0.92) = 0.36 P(gas AND survey says no) = (0.7)(0.12) = 0.084 P(gas|survey says no) = 0.084/0.36 = 0.233 You're really using Bayes' theorem here.

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