this is so stupid

This is a year 9 math question that I was asked...

In a class of 30 children, what is the probability of two students having the same birth month.

So... any two students, any month of the year.

This is what I did first:

30 students
probability of having birthday in any one month = 1/12
probability is the same for all children
so use a Binomial distribution
X~Bin(30, 1/12)
Find P(X=2) = 0.26427
This is the probability.

But it's a year 9 question, right, so we were pretty sure Binomial distribution shouldn't even come into it.

I can't stop thinking about it, and then the answer hits me and I feel so dumb.

Because if you have 30 students, and only 12 months in the year, you're obviously going to have more than one child sharing their birth month with another. There is no way to distribute 30 children between 12 months without having repeats.

The probability has to be 1.


This is what the TEE does to you. It makes you feel smarter than stupid.

But I'm glad it's over :)



[edit] call me sad for not being able to let this go, but is the question asking for exactly two students, or any two students?
I conclude that the wording is ambiguous and I've just wasted ten minutes of my life.