Problem $2-23($Algorithmic$)$

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

$P($ high quality oil $)=0\mathrm{.}60$

$P($ medium quality oil $)=0\mathrm{.}15$

$P(no$ oil $)=0\mathrm{.}25$

a$.$ What is the probability of finding oil? If required, round your answer to two decimal places.

$P($ Oil $)=$

b$.$ After $200$ feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are

$P($ soil $|$ high quality oil $)=0\mathrm{.}15$

$P($ soil $|$ medium quality oil $)=0\mathrm{.}75$

$P($ soil $|no$ oil $)=0\mathrm{.}25$

b$.$ After $200$ feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are

soil $|$ high quality oil