# Math Help - Birthday Probability

1. ## Birthday Probability

Hi guys, I have a question that I was talking about with someone a little while ago. The question is as follows:

If you have 4 people, what is the chances that 2 of them share the same birthday as well as the other 2 sharing a different birthday.

Example:

1st Jan, 1st Jan, 3rd May, 3rd May
or 2nd of March, 20th of December, 2nd of March, 20th December

All people being on the same born on the same day does not count.

2. ## Re: Birthday Probability

The probability that A and B share the same birthday is 1/365. The probability that C and D share the same birthday, but on a different date, is (364/365)(1/365). So the probability that A & B share one date and C & D share another is (1/365)(364/365)(1/365). That's one possible combination of shared birthdays, but there are 2 others: A can share with C and B with D, or A can share with D and B with C. Therefore we multiply the above expression by 3 to get:

$P = 3 (\frac 1 {365})( \frac {364}{365})( \frac 1 {365} ) = 0.0000225$, or one in 44,530.33.

3. ## Re: Birthday Probability

Wow that is a very low chance. That makes sense and thanks for the answer!