Title doesn't make a lot of sense due to the complicated explanation and the fact I tried to be brief.
Basically, I have a Poisson process, and I have been given the information that an event occurred between 9:10:00pm and 9:10:30pm. How do I go about finding the probability that it occurred within the last 10 seconds (i.e. between 9:10:20pm and 9:10:30pm)? (I have the expected number of events at 1 per 5 minutes)
I've tried searching for the probabilities of events in overlapping Poisson intervals, but they don't seem to apply and I can't find anything regarding sub-intervals like the one in this question.
This question is for an assignment due tomorrow and I originally thought I had a correct answer (the probability for an attack within 10 seconds) but the probability was far too low at 0.0322 and I only just realised it was wrong.
It's not just 1/3 is it?