Comparing probabilities in quality management - based on the binomial distribition

Question

Suppose there are two product groups $i=1,2$. The probability that one product chosen at random has a defect is $p_i$. Suppose I chose $Z$ pieces from group $i=1$ and another $Z$ pieces from group $i=2$ (out of $N$ in each group, where $N$ is large, $0 < Z \ll N$ e.g. $Z=1$ to $5$, $N=100000$, and $p < 0.01$). What is the probability that I get more defective products from $i=1$ than from $i=2$ (the conditions may allow for simplifying the calculation to selection with replacement).