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 oil and the test predicts it? 0.09 0.11 0.36 0.44

Answer 1

Since it is stated that the machine he bought only predict about 80%. Thus, about 20% are still possible that there are oils in the land that he owned.
In a 100% value = 80% were the 0 possibillites detected by the machine and 20% are still the possibility that it has an oil.
=> 80% = 0.80
=> 20% = 0.20
In the given choices. letter B has the closest value to the 20% that we expected.
Thus, let's have B as an answer.

Answer 2

C. 0.36

Explanation:

We have been given that owners in the area claim that there is a 45% chance that the land has oil. Jason buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. We are asked to find the probability that the land has oil and the test predicts it.

`P(\text{Land has oil})=(45)/(100)=0.45`

`P(\text{Test predicts that land has oil})=(80)/(100)=0.80`

Since both events are independent, so probability that land has oil and test predicts will be product of probabilities both events.

`P(\text{Land has oil and Test predicts it})=0.45* 0.80`

`P(\text{Land has oil and Test predicts it})=0.36`

Therefore, the probability that the land has oil and the test predicts it would be 0.36 and option C is the correct choice.