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

Answers

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

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

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

[tex]P(A \cap B)[/tex] 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 [tex]P(A) = 0.45[/tex]

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

This means that [tex]P(B|A) = 0.8[/tex]

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

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36[/tex]

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

Answer 2

Answer:

The probability that the land has oil and the test predicts it is 36%

Step-by-step explanation:

So option  C.  0.36 is correct for plato users


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Step-by-step explanation:

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Answers

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