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. If the test predicts that there is no oil, what is the probability after the test that the land has oil

Answer 1

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Let's look at the possibilities: has oil and oil found, has oil but not found, no oil and not found, no oil and false positive.
45% x 20% = 0.45 x 0.2 = 0.09
Therefore, there is only a 9% chance that the land will have oil if the kit claims it doesn't.

Answer 2

Here's y choices
A. 0.1698
B. 0.2217
C.0.5532
D.0.7660

Answer 3

that's not one of my options

Answer 4

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. If the test predicts that there is no oil, what is the probability after the test that the land has oil?

Bayes theorem: P(A |B) = P(B | A ) * P(A) / P(B)

P( has oil | test negative)
= P( test negative | has oil) * P( has oil) / P( test negative)
= .2 * .45 / ( .45 * .20 + .55 * .80)
= 0.16981

Answer 5

thank you