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?
A) 0.1698

B) 0.2217

C) 0.5532

D) 0.7660

Answer 1

If owners told the truth, then the probability is always the same: 0,45.
0,45*0,80 = 0,36

Supposing trust your kit only, then there was 0,8 probability for correct measurement, meaning there is 0,2 chance for incorrect measurement.
If incorrect measurement means displaying a result opposite then truth, then there is 0,2 probability for oil.
If incorrect measurement means displaying a random result (assuming distribution of correct (by fortune) or incorrect answers is 50-50), then there is 0,2*0,5 probability for oil. That is 0,1 probability for oil.

If somehow the answer you are looking for consists of believing the owners and the kit equally, then there are two options. You get both options by applying 0,45 chance to results from previous two cases.
First solution would be 0,2*0,45, that is 0,09 chance.
Second solution would be 0,1*0,45, that is 0,045 chance.

Since none of these answers matches any of given options, I am really interested in calculations by other people. Please do correct me if I made a mistake in my calculations.