There is a vase with $6$ red and $4$ black balls. We choose in a random way $5$ balls, and let $X$ to be the number number of red balls from those we picked. Determine the probability function of $X$, if the sampling done with repositioning.
I am not going through the whole procedure that I followed. So I am just posting my results, and I would be extremely grateful if someone could tell me if its correct and if I should re write in a better way.
So $f(x) = \begin{cases}0.01024 &x=0 \\ 0.01536\cdot a &x=1 \\ 0.02304\cdot b &x=2 \\ 0.03456\cdot c &x=3 \\ 0.05184\cdot d &x=4 \\ 0.0776 &x=5 \\ \text{else } 0 \end{cases}$
where $a,\ b,\ c,\ d$ is the number of times we can find these events happening.
So what do you think pals?
Thanks!