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For each stranger, there is an expectation that the person we have found is Peter Grump at a probability of 1/(200-n) where n is the number of people already asked. If we sum up 1/200 + 1/199 + 1/198 and so on, the point at which the sum totals more than 0.5 is n=77. So by the time we ask the 78th stranger, we would expect to have found Peter Grump. Note that the natural inclination to say it would take 100 strangers, or half the time, is wrong. This is because you are splitting up the room into 100 strangers you will definitely ask. Yes Peter grump has a 50% chance of being in that group, but you also would not continue to ask more people if you had already found him.

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14y ago

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