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 no oil and the test shows that it has oil?

The answers listed are
0.09
0.11
0.44

Answer 1

Well, if we proceed to plan the problem like this:
A = the land has oil B = the kit is not accurate P(A and B) = P(A) * P(B)
Then we can say that (0.45)(1−0.80)=(0.45)(0.20)=0.09
So the answer will be the first one.
I hope this can help you