Question

Select the correct answer.
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 it?
A. 0.09
B. 0.11
C. 0.36
D. 0.44

Answer 1

Answer:

Owners in the area claim that there is a 45% chance that the land has oil. Jason... ... 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.

ANSWER IS B 0.11

Answer 2

Given: Probability of finding oil in Jason's land = 0.45

           Probability of test giving correct result = 0.8

To Find: Probability that land has oil and the test shows the correct result.

Solution:

• Let the Event finding oil be A and

       the  Event that the test shows the correct result be B.

• Here, A and B are two such events where the probability of event A does not affect the probability of event B. Such events are called Independent Events.
• According to the Law of Probability of Independent Events,

         P(A and B) = P(A) . P(B)                (1)

Substituting known values in (1):

         P(A and B) = 0.45 × 0.8

         P(A and B) =  0.36

Therefore, the probability that the land has oil and the test predicts it is option C) 0.36.