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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?

Verified Answer :

Ematio

There is a 36% chance that he will detect oil.

You get this number by taking 80% of 45. I got this by multiplying 45 by .80

Answer:

0.09 or 9%.            

Step-by-step explanation:  

We have been given that 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.

We will use conditional probability formula to get our answer.

We have been given that probability that land has oil is 45% or 0.45.

Let us find the probability that test predicts an inaccurate result. As probability of predicting an accurate test is 80%, so probability that test will be inaccurate will be 100%-80%=20% or 0.20.  

\(\text{Probability that the land has oil and the test predicts it}=0.45\times 0.20\)

\(\text{Probability that the land has oil and the test predicts it}=0.09\)

Therefore, the probability that the land has oil and the test predicts it will be 0.09 or 9%.

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