Assume spam and non-spam email arriving in an inbox can be modelled as two Poisson processes $\{N_1\}$ and $\{N_2\}$ with hourly rates $\lambda$ and $\mu$ respectively.
I am asked to compute the probability that in the next hour three non-spam email will arrive, knowing that $4$ emails have arrived.
I am aware that I can merge the two Poisson processes to obtain another Posson process with rate $\lambda + \mu$; however, I am stuck at this point.
Can anyone give me any help? Thank you for your time!