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? how do you solve this?

Question

anonymous · Answer

Denote $A$ to be the event that oil is present, so $P(A)=0.45$. Then $P(A')$, the complement of $A$, is 0.55.

Denote $K$ to be the event that oil is detected by the kit, so $P(K)=0.80$ and $P(K')=0.20$.

You are asked to find $P(A\cap K)$. Use the conditional probability formula,
$$P(A|K)=\frac{P(A\cap K)}{P(K)},~~P(K|A)=\frac{P(A\cap K)}{P(A)}$$
Of course, you have to determine the conditional probabilities first.

anonymous · Answer

@SithsAndGiggles  so what would be the answer here

anonymous · Answer

i suck at putting formulas in calculator

anonymous · Answer

0.09

0.11

0.36

0.44

anonymous · Answer

I must have misspoke/-typed. The test for oil is 80% accurate, meaning that the test is positive 80% of the time if oil is actually present, so $P(K|A)=0.80$.

Then
$$P(K|A)=\frac{P(A\cap K)}{P(A)}~~\iff~~0.80=\frac{P(A\cap K)}{0.45}~~\iff~~P(A\cap K)=0.36$$

anonymous · Answer

thank you thank you well helped

anonymous · Answer

yw

anonymous · Answer

@jcr268 Wait what was the answer? I don't understand that formula or how to calculate it.

anonymous · Answer

http://openstudy.com/users/jcr268 help plz