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 decid

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?

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  1. Emma
    0
    2021-09-09T01:26:38+00:00

    Let A1 = The land has oil

    A2 = Land has no oil

    B1 = Test Predicted that land has oil

    B2 =Test  Predicted that land has no oil

    Required probability = P(A1/B2)

    A1 and A2 are mutually exclusive and exhaustive.  Hence we can use Baye theorem

    P(A1/B2) = P(A1B2)/P(B2) =

    \frac{P(A1B2}{P(A1B1)+P(A1B2)} =\frac{0.20(0.45)}{(0,20)(0.45)+0.80(0.45)} \\= 0.20[tex]\frac{P(A1B2}{P(A1B2)+P(A1B1)}[/tex]

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