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

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) =

$\frac{P(A1B2}{P(A1B1)+P(A1B2)} =\frac{0.20(0.45)}{(0,20)(0.45)+0.80(0.45)} \\= 0.20$$\frac{P(A1B2}{P(A1B2)+P(A1B1)}$

Answer 2

Answer:

.2217

Step-by-step explanation:

Plato Answer