Given $i=\{A,B,C\}$
$A: n=3, P(\text{Success})=1/8$
$B: n=5, P(\text{Success})=1/4$
$C: n=2, P(\text{Success})=1/2$
And assuming that trials are independent for all $n$, I am trying to find the Variance of the number of times a target will be hit.
To me this seems like a Bernoulli Random Variable, so I assume you can calculate the Variance of hits for all trials as the sum of all variances for each player.
That gives: $$\text{Var}(\text{Hit})=3(1/8)(7/8)+5(1/4)(3/4)+2(1/2)(1/2).$$
Can I calculate the variance of the number of times the target will be hit in this way?