Poisson distribution: trucks and cars _This is some probability problem that I conjured up. Can anyone check whether this problem makes sense and has a solution?_ * * * Assume that the traffic on Spooner street follows a Poisson process with a rate 2/3's of a vehicle per hour. 10% of the vehicles are trucks, the other 90% are cars. Let's say 100 vehicles passed by in Spooner street. In this case, I'm interested in the case where each truck is separated by at least 4 cars. For example: * 'yes' event: `car truck car car car car car truck car` -> there are 5 cars between a pair of trucks * 'no' event: `truck car car truck` only two cars between a pair of trucks What is the probability that these 100 vehicles satisfy the property of having each pair of trucks separated by at least 4 cars?

No, it doesn't make sense, in the sense that the Poisson process doesn't enter into it. Once you know that there were $100$ vehicles, it becomes equivalent to $100$ unfair coin tosses that can come up trucks or cars, and you might as well not mention the Poisson process (in particular its rate) in the first place (unless you made this up to confuse your students :-).