[fnord_too]

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Thanks for the replies!

What I meant in my original post was at least one month without birthdays...any month.

iash

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In that case you have to compute the probabilities of each individual month not having anyone born in it. (Really, there are only 3 cases: 31 days, 30 days, and 28.25 days, but there are 7 31 dayers, 5 30 dayers, and 1 28.25 dayers).

Call these P31, P30, P28, and do the following:
1 - ( (1-P31)^7 * (1-P30)^5 * (1-P28)) to get the probability that there will be no month that has 0 birthdays in it. (Everything following the first "1 - " is the probability that there is at least one birthday in each month.

I think this is slightly off, too, but close. I think this is off because you would have a non zero probability for a month having someone in it if you only had 11 people, so the above would yield a non zero probability of having no month without a birthday in it for 11 people, which is clearly impossible.

hmmm.... my reasoning is off somewhere, but I do not know exactly where.

Here is another attack, for each person you have a probability of that person being born in each month corresponding to the number of days in the month. You could sum over all combinations that have hat least one person in each month (i.e. you could have 79 in january and one in each of the other months C(90,79) ways, 78 in Jan, 2 in Feb, 1 in each other month, etc), but this is a very arduous approach.

I need to reread this thread to see if someone has the right answer already. I'm sure there is an easy way to do this exactly, but I sure cannot think of it right now.