Were you two born in the same month?

Question

Two strangers strike up a conversation. Treat each person's birth month as equally likely to be any of the 12 months, independently. What is the probability that they share the same birth month?

Accepted Answer

Let the first person's birth month be whatever it is; that fixes the target month. The second person's birth month is equally likely to be any of 12 months, and exactly one of them matches. So P(	ext{same month}) = \frac{1}{12} \approx 0.0833, about 8.3\%. The specific month of the first person never enters the calculation. With one month locked in, a single other person matches it with probability 1/12. Takeaway. Coarser buckets mean bigger match odds: months give 1/12 \approx 8.3\%, far larger than the 1/365 for exact days, because there are far fewer slots to land in.

Were you two born in the same month?

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