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For the chance to be at least 50% that two people share the same birthday, there needs to be 22 people. For the chance to be exactly 100% that two people share the same birthday, there needs to be 366 people. If there was 365 people, there would be a very small chance that each person in the room would have different birthdays. With 366 people, there are not enough individual days for every person to have a different birthday, so there has to be at least one pair.

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Q: How many people are needed in a room before two of them share the same birthday?
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