Question

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. If the test predicts that there is no oil, what is the probability after the test that the land has oil?

Answer 1

The probability that the land has oil and the test predicts it is 36%

Explanation:

So for plato users the correct option is C. 0.36

Answer 2

Let A1 = The land has oil

A2 = Land has no oil

B1 = Test Predicted that land has oil

B2 =Test Predicted that land has no oil

Required probability = P(A1/B2)

A1 and A2 are mutually exclusive and exhaustive. Hence we can use Baye theorem

P(A1/B2) = P(A1B2)/P(B2) =

`(P(A1B2)/(P(A1B1)+P(A1B2)) =(0.20(0.45))/((0,20)(0.45)+0.80(0.45)) \\= 0.20`
`(P(A1B2)/(P(A1B2)+P(A1B1))`