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.

Question

1 month ago

6

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?

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-04-05T14:52:40+03:00

<span>There is a 45% -------------------------------probability that the land contains oil

then
55</span>%--------------------------------probability that the land does not have oil

80% -------------------accuracy in detecting oil in the soil (if it is present)<span>20</span>% -------------------accuracy in indicating no oil in the soil (if oil is present)

20% ---------------------accuracy in suggesting oil exists in the soil (if there is none)
80% ---------------------accuracy rate for indicating no oil in the soil (if absent)

the chance that the land has no oil----------------55%
the test indicating oil-------- 20%
hence 0.55*0.20=0.11=11%
the likelihood that the land is devoid of oil while the test shows it has oil is 11%