There are 3 red, 9 green balls in the box. We pick them randomly without returning. When take out red ball for the first time we stop. X-discrete distributed variable, where we have the number of taken balls before we take out first red ball.
What is the probability distribution for X?
So we can write $X$ is the following way:
$X= I_1+I_2+...+I_9$, where $I_i = 1$ if we take out green ball and $I_i=0$ otherwise. Hence $P(X) = P(I_1+...+I_9) = P(I_1=1)+ ... + P(I_9 =1)$. Now the probability green ball is drawn is $9/12$ hence $P(I_i=1) = 9/12$,$P(I_2=1)=8/11$..