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## Saturday, July 26, 2008

### Baffling Birthdays

In Mrs. Melanie's class are twenty-six children. None of the children was born on February 29th.

The Question: What is the probability that at least two children have their birthdays on the same day?

Answer: The probability that at least two children have their birthdays on the same day, is 1 minus the probability that all children have their birthdays on different days. Therefore, we first calculate the latter probability.

None of the children was born on the 29th of February, so there are 365 days on which each child could have its birthday. The first child can have its birthday on any day (probability 1). The second child must have his its birthday on a different day than the first child; the probability for that is 364/365. The third child has to have its birthday on again a different day than the first and second; the probability for that is 363/365. Continue like this till the 26th child with a probability of 340/365. The total probability then becomes 1 × 364/365 × 363/365 × ... × 340/365 (about 40 percent).

The probability that at least two children have their birthdays on the same day, is 1 minus above-mentioned probability, around 60 percent.