# Probability of death for individual in group

I was never good with probability. I have this question which is not a homework. Let's say we have a set of $$N$$ people. Each has a probability $$p$$ to die at a given moment. What is the probability that a given person $$x$$ from the set of $$N$$ people dies before the remaining $$N-1$$ persons?

I am not sure where to start? In fact I am not sure $$N$$ plays a roll here? Thanks.

Note: Death can occur at any moment.

• Does death "check every 5 seconds, whether someone's time has come", or can people die at any moment (in a "continuum of moments")? Dec 2, 2022 at 10:57
• in a "continuum of moments"...like real life :) Dec 2, 2022 at 11:01
• Then I don't think that "checking at each point in a continuum" is a good mathematical model. What comes to mind is, for example, the exponential distribution (en.wikipedia.org/wiki/Exponential_distribution; for the waiting time until an event occurs). But realistically, the probability that two people die at the exact same time is $0$, so someone is bound to die before everyone else. Because of symmetry, for any person involved, the probability of being the "winner" of this race is $\frac{1}{N}$. Unless you meant that different people have different $p$'s. Dec 2, 2022 at 11:15
• @nasekatnasushi, It is questionable if N is relevant, as long as $N>=2$, so $P($x$_dies_before_$y$)$, $N=2$ is no different than if N=3 for example. Accordingly $1/N$ may not be correct in this case. Dec 2, 2022 at 13:03
• You say in the comments that there is a "continuum of moments". This suggests that the probability that a given person dies at a given moment is $0$. That is $p=0$. So that leaves the question: What is the distribution of death times? Having said that, I agree with nasekatnasushi, that if everyone has the same death distribution, then the probability that any specific person is the first to die is $\frac1N$. Regarding the subsequent comment of NoChance: the events of various people dying before various other people are not independent. Dec 2, 2022 at 13:40