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# The Birthday Problem and Some Generalizations

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:
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.

### PERMANENT CITATION

Contributed by: Marc Brodie (Wheeling Jesuit University)
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#### Related Curriculum Standards

US Common Core State Standards, Mathematics

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