## Exoected Time to Get Facebook Likes

Most people, when they visit most Facebook pages, are not very interested. They don't find much reason to either like or dislike the page. Given however, that a page can either be liked or disliked, how long will it be before a certain number of likes,
$N$
is reached?
Suppose that a page has
$n$
visitors per day. The probability of a person liking the page is
$p$
and the probability of someone disliking it is
$p$
. Suppose also that these two probabilities are independent. The expect number of likes in a day is
$np$
and the expected number of dislikes in
$nq$
. The expected number of net likes is
$np-nq=n(p-q)$

The in will be an estimated
$\frac{N}{n(p-q)}$
days before you get
$N$
$q \gt p$