0
$\begingroup$

The title states the full question I was provided with. Am I able to just assume the class contains more than 12 students? If so, would we just do:

(n choose 2?); where n = number of students in class?

If not, how else could I go about this? Do I need to break it into more than 1 case? I know the solution is probably very simple, I just don't know if I am thinking about this in the right manner.

$\endgroup$
4
  • 2
    $\begingroup$ This is called the birthday problem. The wiki page contains the information you need. $\endgroup$
    – user347499
    Jun 14, 2016 at 18:39
  • $\begingroup$ "Am I able to just assume the class contains more than 12 students?" - Now why would you ever assume that??? If anything, you may want to assume "more than $1$ student" (otherwise, obviously, the probability is $0$). In order to find the general formula for $n$ students, calculate $1$ minus the probability of the complementary event: $1-\frac{365!}{(365-n)!\cdot365^{n}}$. BTW, with $n=23$, the probability is just a little over $50\%$, which is why this is generally referred to as the Birthday Paradox (considered a paradox because people normally expect a lot more than $23$ here). $\endgroup$ Jun 14, 2016 at 19:50
  • $\begingroup$ You assume the class has n students an's express the answer in terms of n. If you assume n=12 you will get a precise number. If you assume n=20 you will get another. Not sure where you got 12 from. $\endgroup$
    – fleablood
    Jun 14, 2016 at 20:48
  • $\begingroup$ n choose 2 isn't the answer by the way. It doesn't make sense. $\endgroup$
    – fleablood
    Jun 14, 2016 at 20:50

1 Answer 1

1
$\begingroup$

This image should answer your question.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.