I have a website and I want to calculate the probability of clicks on the ads.

Let the probability that each user clicks on a link be p (something like 1%)

if we have totally N users, What is the formula that computes the probability of exactly n clicks? of course we have

0< = n <= N

Each users can click only once


1 Answer 1


Consider each user as a trial. For every trial you have two outcomes, they are success (clicks on ad) and failure (does not click on ad). $P[success] = p $ and $P[failure] = 1-p$.

The total number of ways in which $n$ users can be selected from $N$ users is $\binom{N}{n}$. So, the probability of exactly $n$ clicks is $\binom{N}{n}*p^n*(1-p)^m$ where $m = N-n$, as the clicks are independent and exactly $n$ clicks mean exactly $N-n$ 'not clicks'.

  • 1
    $\begingroup$ And this is called the binomial distribution. $\endgroup$
    – ken
    Oct 11, 2018 at 20:51
  • $\begingroup$ Yes @Ken sure it is!. $\endgroup$
    – naive
    Oct 12, 2018 at 14:35
  • $\begingroup$ Thanks @naive, is there any function to get (N n) for large Ns. (calculating N! for large Ns is impossible) an approximate function would be sufficient. $\endgroup$
    – Ormoz
    Oct 27, 2018 at 18:28
  • $\begingroup$ For large $N$ the binomial random variable can be described by a Normal distribution. $\endgroup$
    – naive
    Oct 28, 2018 at 7:28

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