The wording of the second question is fucked-up:
Quote:
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Originally Posted by xxweekxx
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow:
P ( soil | high quality oil) = .20
P(soil | medium-quality ) = 0.80
P(soil | no oil) = 0.20
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?
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"The probabilities of finding the particular type of soil identified by the test follow:" -- not clear.
I'm going to assume, then, that the new set of probabilities are simply a latter-phase adjustment of the orginal set, and NOT intended to introduce any conditional probability (based on the accuracy of the test) as a function of the first.
If that's the case, then all we have is simply a RESTATEMENT of the probability set with weighted likelihood nested inside an A vs. B (binary) outcome.
The 2 possible binary outcomes are OIL=yes, and OIL=no. Since we are told that the probability of OIL=no is 20%, we must apply the remaining probabilities ONLY to the remainin OIL=yes binary contingency.
The solution is simply that the remaining 80% probability that there will be ANY oil (100% - 20% OIL=no) is itself subject to a SECONDARY probability, to be applied only in the case that ANY oil is found.
Hence, 80% probability of medium OIL + 20% probability of quality OIL = 100%, in the case ANY OIL is found.
New probability set:
MEDIUM = 64% (80% * 80%)
HIGH = 16% (20% * 20%)
NO OIL = 20%
j-