# Probability to get always the same number choosing randomly from a set of $c$ elements

What is the probability to get $n$ times the same element $k$ choosing randomly from a set $A$ knowing the cardinality $|A| = c$?

It depends: is $k$ fixed in advance? if so then the probability is given by $\frac{1}{c^n}$. If you just ask for the probability to have $n$ times the same element, then it is $\frac{1}{c^{n-1}}$ (since the first time you can have any object). By the way, I supposed you are doing exactly $n$ tries. Of course, the probability changes if you are doing more than $n$ tries.
• Thank you! But why does it change if $k$ is fixed? Nov 2, 2010 at 15:33
• @rubik: if $k$ is fixed IN ADVANCE, then the first time you must choose it. If $k$ is not decided in advance, then you just ask that starting from the second draw you get the same object as the first time. Thus, the first draw can be anyting. Nov 2, 2010 at 15:38
Assuming that you draw $n$ times uniformly at random from the set of $c$ elements, it is $\frac{1}{c^{n-1}}$ as Djaian says. You are rolling a $c$-sided die.