I'm told that the probability of getting $n$ murders per month in London can be modelled as a Poisson distribution with rate $\lambda$. I'd like to calculate the probability that, in a month with 5 murders, there were no murders within the first week. I thought this would simply equal the probability that there are no murders in a week multiplied by the probability that there are 5 murders in the (remaining) three weeks. Is this correct? If not, what should I be doing instead?