Oscar的狗丢失在丛林中(条件与独立性概率习题)

Oscar在森林A(0.4概率)或B(0.6概率)失去了他的狗。第一天在A森林找到狗的概率是0.25,在B森林是0.15。狗在第n天活着的概率为2^(n+1)。Oscar根据一系列条件决定在哪个森林搜索,并考虑了狗可能的生存状况。问题包括:首次搜索应选择哪个森林、第一天未找到狗时狗在A森林的概率、通过抛硬币决定搜索地点找到狗时在A森林的概率、连续两天在A森林找狗在第二天找到活狗的概率,以及第四天找到狗时,前三天在A森林且第四天在B森林找到活狗的概率。

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题意如下

Oscar has lost his dog in either forest A (with probability 0.4) or in forest B (with probability 0.6).

If the dog is in forest A and Oscar spends a day searching for it in forest A, the conditional probability that he will find the dog that day is 0.25. Similarly, if the dog is in forest 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 overnight.

The dog is alive during day 0, when Oscar loses it, and during day 1, when Oscar starts searching. It is alive during day 2 with probability

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