Probability of event happening after the last event

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.

• I assume what you mean by intervals are known is time between events have known distributions, then you should look for the probibility that time between events is less than 20 from the corresponding cdf if time between events are independent. Otherwise your question and approach makes no sense to me at all. – Bob Nov 26 '14 at 17:04
• Are you working with data or is this a homework question? – wolfsatthedoor Nov 26 '14 at 17:36
• The probability is 1 unless you are bounding your time frame in some way: humans die pretty quickly without water (for broad definitions of water :). – Alexis Nov 26 '14 at 18:15