# how to calculate the following conditional probability

There are two events involved, say event A and event B. I want to know the probability of event B conditioned on the event A. The relation between the two events are as follows. We can not talk about about event B if event A does not happen, for example, we can not talk about the probability of death of a person if that person is not born yet. Moreover, once A happened, the events A and B are basically independent. Well, almost independent. For example, once a person is born, the probability of that person's death only has relation with the specific time when that person is born, not with the event of the birth of that person. I hope I explain it clearly enough. Any directions for future references are greatly appreciated. Many thanks for your time and attention.

"B cannot happen until A happens" is the same as 'B is contained in A' or 'B is a subset of A' or 'B is equal to A'. (I'm thinking in terms of Venn diagrams)

When one event is a subset of another, they cannot be independent.

But you can still think of this as two circles intersecting (one for birth and another for time) and the common area to be the event of death (assuming a particular region of time can cause death). Then you can find the probabilities. [here I have three variables- birth, death and time]

I do not have much knowledge about time being incorporated as such in conditional probabilities

PS. I wanted to post this as a comment, but don't have the reputation yet!

• Could you elaborate more about the point that "assuming a particular region of time can cause death"? Jun 17 '15 at 13:22
• I am assuming death can happen at a particular time range instead of a particular time. Because 'time range' can be equated to a 'region' whereas a 'particular time' will refer to a 'single point on the plane' in Venn Jun 17 '15 at 14:18
• The reason I asked this question is because I wanted to estimate the probability of the death of a person after it was born. I guess I can try to approximate it a little bit by assuming that a person would die after living sufficiently long (like 60 years), so this is like what you mentioned that assuming a particular region of time can cause death. Then, this would be like deterministic in some sense, is it appropriate? Jun 18 '15 at 12:09
• Yes, you can calculate the probability only by adding the time variable. Otherwise, the probability that a person will die after he/she is born is 1. Jun 18 '15 at 12:17