Consider a poisson process one (P1) with a frequency 'a' and if it happens 'k' times you get (e^-a)(a^k)/k! and then you have another posssion processs that happens in the same time frame of P1 called P2 with a frequency of 'b' and if it happens 'z' times you get (e^-b)(b^z)/z! So what is the probability that P1 merges with P2? For example if is observed that a computer breaks once every 2 days and a lightbulb goes out every 4 days what is the probability that in one week two computers will break at the exact same time 5 lightbulbs go out? I know this problem has something to do with the poisson distribution but I dont know how to merge these events to get an answer. I went to wikipedia and searched on the net and couldnt find any exmaples of such a problem that deals with two events. I found somethign on wikipedia that says: If N and M are two independent random variables, both following a Poisson distribution with parameters λ and μ, respectively, then N + M follows a Poisson distribution with parameter λ + μ. I know the the probabilities of both events happening are less than the probability of just one, but I dont think you can just multiply the probability of event each together to get the final probability of both events happening at the same time.