Suppose that it arrives people to a store according to a poisson process with rate $\lambda = 6$/hour , females arrive with probability $0.6$ and male with $0.4$.
What is the probability that there are 4 male and 3 female persons in the store at time $t = 20 $ minutes
here is my answer,which is wrong, maybe someone can explain why?
I know that I can regard Female arrivals as its own poisson process with rate ($0.6*6$)/hour and Male arrivals with rate ($0.40*6$)/hour. let us denote these two poisson processes as ,female : $\{ N_1(t),t\geq 0 \}$ and male: $\{ N_2(t),t\geq 0 \}$.Furthermore I know these are independent.
So i want this probability : $P\{N_1(20) = 3,N_2(20) =4 \}$ by independence i get $P\{N_1(20) = 3\}*P\{N_2(20) =4 \}$ but this is wrong why??