Consider two people being randomly selected. (For simplicity, ignore leap years.)?

Question

Consider two people being randomly selected. (For simplicity, ignore leap years.)

What is the probability that two people born in September have a birthday in the first half of the month?

Answer 1

Are we assuming that the two people randomly selected have birthdays in September? Then the chances are .25 that they are both in the first half.

If we are are not assuming that then it would be (15(days in the first half of September)/365(days in the whole year))^2
(15^2)/(365^2)=about .0017

Both of these solutions assume that there is an even distribution of births over the year...which is unfortunately not true...

Answer 2

Chance a person is born in half of month x:
1 to 24 (12 months, 24 half months per year)

Estimated chance two persons would be born in half of month x:
1 to 24 * 24 = 1 to 576