the very basic probability on not being born in May

The Facebook question was "What's the chance one of my Facebook friends was born in May?" My answer: Months that are not May = 11. The month that is May = 1, the number of Facebook friends I have = 350. Therefore, P(A) where A=none of my Facebook friends was born in May, P(A)=(11/1)^350. I say that is a probability of 9.15537170E+150/1 So, very likely one of them was born in May.

Am I wrong?

• There seems to be a typographical error: didn't you mean to write "$(11/12)^{350}$" instead of "$(11/1)^{350}$"? The former equals $6\times 10^{-14}$ while the latter is nonsensical.
– whuber
May 8, 2018 at 20:14

Assuming all of your friends' birthdays are independent of each other (no twins), the probability of any one of them NOT being born in May is approximately $11/12$. That is, if its equally likely to be born in any month, you have a 11 out of 12 chances to be born in not-May.
So, the probability that NONE are born in May is ~$(11/12)^{350}$. That implies that the probability that at least one is born in May is $1-(11/12)^{350}$, which is indeed very likely.