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. What is the probability that the land has no oil and the test shows that it has oil?

Answer 1

45% -------------------------------chance that the land has oil

then
55%--------------------------------chance that the land not have oil

80% -------------------accuracy rate of indicating oil in the soil. (if land does have oil)
20% -------------------accuracy rate of indicating not oil in the soil. (if land does have oil)

20% ---------------------accuracy rate of indicating oil in the soil. (if land has not oil)
80% ---------------------accuracy rate of indicating not oil in the soil. (if land has not oil)

 that the land has no oil----------------55%
 the test shows that it has oil-------- 20%
then 0.55*0.20=0.11=11%
the probability that the land has no oil and the test shows that it has oil is 11%