Mr. Jow:
       I still believe your initial answer of 1 is correct. Even if the first
12 people have 12 different birth months, the 13th person will have to share
a birth month with one of the first 12 people.
The probability in question is 2 people are born in the same month and not
the probability that they have the same birthday!
    Peace!
            Amat

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