A box contains $20$ balls all of different colors including the red color. If we select $10$ balls randomly without replacement, what is the probability that the red ball will be among these $10$ balls?
What I think is that: If we let $X$ to be the number of balls we select until we get the red ball, then $X$ will be a random variable with range $ 1,2,3, \ldots ,20 $, and the probability of getting the red ball will be $1/20$, so our probability will be $$\left(\frac{1}{20} \right)^{10} ,$$ is that right?! I'm not sure about the distribution of $X$?