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 88% of the time correct when gas was indeed present and 92% 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.

If anything just tell me what distributtion to use.....THANKS

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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