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assignment-03

# assignment-03 - Third Problem Assignment EECS 401 Problem 1...

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1 Third Problem Assignment EECS 401 Problem 1 Oscar has lost his dog in either forest A (with a priori probability 0.4 ) or in forest B (with a priori probability 0.6 ). If the dog is alive and not found by the N th day of the search, it will die that evening with probability N/ ( N + 2 ) . If the dog is in A (either dead or alive) and Oscar spends a day searching for it in A , the conditional probability that he will find the dog that day is 0.25 . Similarly, if the dog is in B and Oscar spends a day looking for it there, he will find the dog that day with probability 0.15. The dog cannot go from one forest to the other. Oscar can search only in the daytime, and he can travel from one forest to the other only at night. All parts of this problem are to be worked separately. (a) In which forest should Oscar look to maximize the probability he finds his dog on the first day of search? (b) Given that Oscar looked in A on the first day but didn’t find his dog, what is the probability that the dog is in A ? (c) If Oscar flips a fair coin to determine where to look on the first day and finds the dog on the first day, what is the probability that he looked in A ?

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