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 no oil and the test shows that it has oil?

Answer:0.36 = 36% probability that the land has oil and the test predicts itStep-by-step explanation:Conditional ProbabilityWe use the conditional probability formula to solve this question. It is[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]In whichP(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.45% chance that the land has oil.This means that [tex]P(A) = 0.45[/tex]He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.This means that [tex]P(B|A) = 0.8[/tex]What is the probability that the land has oil and the test predicts it?This is [tex]P(A \cap B)[/tex]. So[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex][tex]P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36[/tex]0.36 = 36% probability that the land has oil and the test predicts it