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 it

Answer 1

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ 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 $P(A) = 0.45$

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that $P(B|A) = 0.8$

What is the probability that the land has oil and the test predicts it?

This is $P(A \cap B)$. So

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36$

0.36 = 36% probability that the land has oil and the test predicts it