How to Calculate the Probability of 13 Out of 408 Guessing a Birthday Correctly?

[Arbu]

If 408 people try to guess someone's birthday, how do you calculate the chance of 13 of them being right? http://www.greasypalm.co.uk/gpforum/forum14/363.html

 

[0rthodontist]

Well, the chance of each individually being right is 1/365 (ignoring leap years and assuming people's guesses are independent of the person's actual birthday, which is probably not true), and if they are independent then it follows the binomial distribution, so the answer is
C(408, 13) * (1/365)^13 * (364/365)^395. Unless you're interested in the probability of at least 13 being right.

 

[Arbu]

Sorry, statistics represents a bit of a gap in my education. What is this C function, and how do I calculate it/look it up?

Let's go with exactly 13 of them being right.

 

[ksinclair13]

C(n, k) = \frac{n!}{(k!)(n-k)!}

 

[Arbu]

Thanks. 1 in 5,370,675,393 I make it.