Answer:
0.36 = 36% probability that the land has oil and the test predicts it
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
45% chance that the land has oil.
This means that [tex]P(A) = 0.45[/tex]
He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.
This means that [tex]P(B|A) = 0.8[/tex]
What is the probability that the land has oil and the test predicts it?
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36[/tex]
0.36 = 36% probability that the land has oil and the test predicts it
