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 that there is no oil?

Answer 1

The probability that the land has oil and the test predicts that there is no oil is:

0.09

Explanation:

The test claims that there is 80% accuracy rate of indicating the oil.

This means that the test does not predict the correct rate is: 20%

Also, the percent chances that the land has oil is: 45%.

Let A denote the event that the land has oil.

Let B denote the event that the test predicts the wrong result.

Let P denote the probability of an event.

Hence, from the information we have:

P(A)=0.45 and P(B)=0.20

We are asked to find:

P(B∩A)

We know that as both the events are independent.

Hence, P(B∩A)=P(A)×P(B)

Hence, P(B∩A)=0.45×0.20

⇒ P(B∩A)=0.09

Hence, the required probability is:

0.09

Answer 2

0.45*0.2= 0.09
so probability that there will be oil after the test= 0.09 %