Do these two coworkers share a birthday?

Question

Two coworkers meet for the first time. Assume every birthday is equally likely and independent across $365$ days (ignore leap years).

What is the probability that the two of them were born on the same day of the year?

Accepted Answer

Fix the first person's birthday, whatever it happens to be. Now the only question is whether the second person lands on that exact same day. The second person's birthday is equally likely to be any of the 365 days, and exactly one of those days is a match. So P(	ext{same birthday}) = \frac{1}{365} \approx 0.0027, or about 0.27\%, roughly 1 chance in 365. Notice we did not need to know what the first birthday actually was. Once one date is locked in, the match probability for a single other person is always 1/365. Takeaway. For two random people the chance of a shared birthday is just 1/365. …

Do these two coworkers share a birthday?

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