My question seems to be very trivial, but I'm still stuck with it. It's about probability calculations. Suppose you have a number of people that take a glass of water (event), time between 2 events is known (intervals) and events are not independent. I want to calculate probability of a person taking a glass of water in the next 20 minutes (number of minutes can vary) after the last event. I tried to use:
Probability = (number of intervals > i and < i + 20 minutes)/number of all intervals
where i = 0, 1, 2, 3, ...seconds
However, my probability tends to decrease with time, however I expect it to rise. Could someone please advice me on it.