Let $x_1, x_2,..., x_m$ be iid binomial random variables (each with a number of trials n and probability of success in each trial p). Define a list of binary indicator variables $y_1,y_2,...,y_m$ for at least $K$ successes i.e.,

$ y_i = \begin{cases} 1 & \text{if } x_i\geq K\\ 0 & \text{else} \end{cases}$

What is the variance of $z=\sum_1^m y_i$ ?