195.The Fifth Fish
★★★conditional probabilityJane Street
A bear stands at a river and wants three fish. Fish swim past one at a time, and the bear catches each one it attempts with probability one half, leaving immediately once it has caught its third. What is the probability that the fifth fish to swim past is not caught?
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The fifth fish escapes in two separate ways: the bear may already have left, or it may still be there and simply miss.
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