Solution to: Baffling Birthdays

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 February 29, 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 until the 26^th 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.

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