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far far away
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Here's a question makes me confused.
A bird leaves its home to find some food. It won't return if it doesn't find any food. Suppose the probability it returns in the first day is 1/2 and returns in the second day is 1/4 and returns in the third day is 1/8 ... returns in the nth day is (1/2)^n.
The total probability it will return is 1/2+1/4+1/8+1/16+...(1/2)^n+...=1. That means the bird absolutely will be back someday in the future. But if the bird doesn't come back in the first day then the probability it would come back would be 1/2 and that means it has the chance to not come back. Moreover, if the bird doesn't come home in the first few days then the chance it come back would become really small and that means it nearly won't come back. But how could the bird will be back and it won't be back at the same time
I was studying one dimensional random walk. I think the question is kind of similar. Thanks
A bird leaves its home to find some food. It won't return if it doesn't find any food. Suppose the probability it returns in the first day is 1/2 and returns in the second day is 1/4 and returns in the third day is 1/8 ... returns in the nth day is (1/2)^n.
The total probability it will return is 1/2+1/4+1/8+1/16+...(1/2)^n+...=1. That means the bird absolutely will be back someday in the future. But if the bird doesn't come back in the first day then the probability it would come back would be 1/2 and that means it has the chance to not come back. Moreover, if the bird doesn't come home in the first few days then the chance it come back would become really small and that means it nearly won't come back. But how could the bird will be back and it won't be back at the same time
I was studying one dimensional random walk. I think the question is kind of similar. Thanks