Matching your birthday specifically

Question

Birthdays are spread evenly over 365 days (no February 29). How many other people must be in the room before it is more likely than not that at least one of them shares your exact birthday?

Accepted Answer

Now the target is fixed: your birthday. Each other person misses it with probability 	frac{364}{365}, independently, so with n other people P(	ext{nobody matches you}) = \left(\frac{364}{365}ight)^n. You want this below 	frac12: \left(\frac{364}{365}ight)^n < \frac12 \;\Longrightarrow\; n \frac{\ln 2}{\ln(365/364)} \approx \frac{0.6931}{0.002743} \approx 252.6. So n = 253 people are needed for better-than-even odds that someone shares your birthday. Compare this with the 23 needed for any two people in the room to match. Matching a specific date is roughly ten times harder, because you…

Matching your birthday specifically

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