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?

Answer 1

Answer: The probability after the test that the land has oil is 0.09.

Explanation:

Let A is the event that the land has oil.

It is given that there is a 45% chance that the land has oil. So,

$P(A)=\frac{45}{100}$

The probability that the land has no oil is,

$P(A)=[tex]P(A')=1-P(A)=1-\frac{45}{100}=\frac{100-45}{100}=\frac{55}{100}$

Let B is the event that the kit gives the accurate rate of indicating oil in the soil. So,

$P(B)=\frac{80}{100}$

The probability that the kit gives the false result is,

$P(B')=1-P(B)=1-\frac{80}{100}=\frac{100-80}{100}=\frac{20}{100}$

Events A and B are two independent events and we have to find the probability that the last has oil and kit given false result.

$P(A\cap B')=P(A)P(B')$

$P(A\cap B')=(\frac{45}{100})(\frac{20}{100})=\frac{900}{10000} =\frac{9}{100}=0.09$

Therefore, the if the test predicts that there is no oil, then the probability after the test that the land has oil is 0.09.

Answer 2

The options are

A.

0.1698

B.

0.2217

C.

0.5532

D.

0.7660