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Consider the problem facing a park service if someone is reported to have entered a wilderness...

Consider the problem facing a park service if someone is reported to have entered a wilderness area and not returned. The service may mount a search by considering different regions that cover the park and searching in them sequentially. For the jth region, there is a probability pj that the missing person will not be found even if s/he is in the region. Suppose that the park is divided into four regions, and that the park service estimates that the missing person has an equal chance of being in any of the four regions.

(a) If they search the first region and fail to find the missing person, what is the conditional probability that the person is actually in that region? In each of the other three regions?

(b) Now suppose that the park service searches the second region as well and also fails to find the missing person. What is the probability that the person is in the first region? The second? The third? Fourth?

math   Statistics-And-Probability   
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