Question

An oil explorer performs a seismic test to determine whether oil is likely to be found in a certain area. The probability that the test indicates the presence of oil is 90% if oil is indeed present in the test area and the probability of a false positive is 15% if no oil is present in the test area. Before the test is done, the explorer believes that the probability of presence of oil in the test area is 40%. Use Bayes’ rule to revise the value of the probability of oil being present in the test area given that the test gives a positive signal.

Answer 1

Answer:

By using bayes' rule the value of probability of oil being present is 0.8 .

Answer 2

$0.8$ is the value of the probability of oil being present in the test area given that the test gives a positive signal.

Given:

The probability that the test indicates the presence of oil $=90$%$=0.9$

Probability of a false positive $=15$ %$=0.15$

Probability of presence of oil in the test area $=40$%$=0.4$

To Find:

The value of the probability of oil being present in the test area given that the test gives a positive signal.

Step-by-step explanation:

Test in presence of oil,

$\[0.9\times 0.4=0.36\]$

Value of the probability of oil being present in the test area,  

$\[ & 0.15\times (1-0.4)=0.09 \\ & 0.36+0.09=0.45 \\ \end{align}\]$

The test gives a positive signal , $\[{{T}_{P}}=0.45\]$

Use Bayes’ rule to revise the value of the probability of oil being present in the test area given that the test gives a positive signal.

$\[P(O|{{T}_{P}})=\frac{0.36}{0.45}=0.8\]$

Hence,$0.8$ is the value of the probability of oil being present in the test area.