\[N\]

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 \[N\]

Facebook likes. If \[q \gt p\]

then you probably have more dislikes than likes and your threshold may never be reached.