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 shows that there is no oil? A. 0.09 B. 0.11 C. 0.44 D. 0.36

Answer 1

Probability that the land has oil and the test shows that there is no oil is 0.09.

Step-by-step explanation:

We are given that 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.

Let the Probability that the land has oil = P(O) = 0.45

Probability of the testing kit indicating oil in the soil = P(A) = 0.80

Probability of the testing kit indicating no oil in the soil = P(A') = 1 - P(A) = 1 - 0.80 = 0.20

Now, the probability that the land has oil and the test shows that there is no oil is given by = Probability that the land has oil $\times$ Probability of the testing kit indicating no oil in the soil

                              =  P(O)  $\times$  P(A')

                              =  0.45  $\times$  0.20

                              =  0.09

Hence, the probability that the land has oil and the test shows that there is no oil is 0.09.