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 that there is no oil?

Answer 1

The probability that there's no oil os 9%

Explanation:

So for plato users option B. 0.09 is the correct option

Answer 2

9% or 0.09

Explanation:

• Given, chance of land having oil is 45%. Which is 0.45

So, chance of land NOT having oil is
`100-45=55` percent. Which is 0.55

• Given, kit's accuracy rate of finding oil as 80%. Which is 0.80

So, kit's accuracy rate of NOT finding oil is
`100-80=20` percent. Which is 0.20

These 2 events are INDEPENDENT, which means that the probability of one event occurring does not affect the probability of another event occuring.

The formula, if we let the two evens be A and B, is:

P(A and B)=P(A) * P(B)

Now, "the probability that the land has oil (event A) AND the test predicts that there is no oil (event B)" will be:

P(A and B) = P(A) * P(B)

`=(0.45)(0.2)=0.09`

Hence, the probability is 0.09 or 9%