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. What is the probability that the land has oil and the test predicts that there is no oil?

Answer 1

you are given the probability of the test indicating oil but we want the probability of the test ~not~ indicating oil

therefore: probability of no oil indicated = 1 - probability of oil indicated

for two independent events, P(A and B) = P(A)P(B)

so probability that the land has oil and the test predicts that there is no oil =

(probability of land having oil) * (probability of test predicting no oil)

= (probability of land having oil) * (1 - probability of oil indicated)

plug in the appropriate values from the problem to find the solution