The Birthday Problem and Some Generalizations

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The birthday problem asks, "How many randomly selected people must there be in a room in order for the probability that two people share a birthday to exceed 0.5?" and has the well-known answer 23. The following generalizations are illustrated here, along with answers:

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1. The probability of 0.5 can be replaced by any value from 0.01 to 0.99, in increments of 0.01.

2. The number of days in a year can be any value from 2 through 5000, for the convenience of extraterrestrials.

3. The question "How many randomly selected people must there be in a room in order for the probability that two people share a birthday or have birthdays on consecutive days to exceed 0.5?" is investigated.

Any combination of these generalizations can be used simultaneously.

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Contributed by: Marc Brodie (Wheeling Jesuit University) (March 2011)
Open content licensed under CC BY-NC-SA


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