I understand how to work out probabilities where the number is greater than a given value, now I'm trying to work out how to get the probability of something less than a given value happening.
The simple answer is to just work out the greater than value, and subtract that from 1 to get the less than value, however this is missing the "equal to" part.
If I just work out "what is the probability that a given event will happen less than 3 times" I could work out the probability that it will happen more than 3 times, and subtract that value from 1. However doing that I will calculate the probability of the event happening less than or equal to three times.
How can I calculate an event happening just less than (not less than and equal to) - for example less than three times?
Example: cars crossing a junction during daylight hours may be modelled as a Poisson process with the rate of four per hour. What is the probability that the gap between two successive cars will be more than 20 minutes but less than 30 minutes?