I have $n_1$ red balls and $n_2$ blue balls in a box.
Randomly select $k$ balls from the box. What is probability selects red balls only?
My solution is:
Let $X$ be event that select red ball only. $R$ is number of selected red ball. The probability of the event $X$ is
$$P(X)=\sum_{i=1}^{n_1} P(R=i)=\sum_{i=1}^{n_1} \frac{\binom{n_1}{i}}{ \binom{n_1+n_2}{i}}$$
Is my solution correct? Thank all