I am struggling with understanding a certain result. I study poisson processes, and a solution to an exercise I am doing does not make sense to me.
Let $N_1(t)$ be a Poisson($\lambda$) process and $N_2(t)$ a Poisson(3$\lambda$) process that are independent. Then
$$P(N_1(h)=1,N_2(h)=0)=(\lambda h+o(h))(1-3\lambda h+o(h))=\lambda h+o(h)$$
What I don't understand is the last equality. How to we derive that? Thank you.