Question

Select the correct answer. 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 choices : a, 0.1698 , b 0.2217, c 0.5532, d 0.7660

Answer 1

Option A 0.1698

Explanation:

Given that Jason has a chance for getting oil as 45%

THe kit he buys show accurate result with 80% probability

Let A1- Event that the land has oil

A2 - Event that the land has no oil

B- The test gives negative result

A1 and A2 are mutually exclusive and exhaustive

P(A1) = 0.45 and P(A2) =0.55

Hence we can use Baye theorem

Then P(B) = P(A1B)+P(A2B)=
`0.45(0.20)+0.55(0,80)\\=0.09+0.0.44\\=0.53`

Reqd prob =P(A1/B) =

`(P(A1B))/(P(B))\\ =(0.09)/(0.53)\\\\=0.1698`