Depends upon how close the closets two are to each other which could vary dramatically.

Btw as a heads up... none of the calculations, no matter how likely have taken into account age distribution as well as population distribution. Based on Wikipedia statistics only 66% of people are aged 15-64 and these people are likely the only ones capable of finding another person. So out of your 35 people, only 23 of them are going to be capable of actively searching for other survivors.

The age point is a good one, though depending on why only 35 people people are left, the survivors may be self-selected for a hard immune system, which would weight the age towards 20's-30's.

if you are lucky, none of the survivors find themselves alone in any means of transportation, because their chance of surviving long enough to wonder whether or not they are alone are ot very good.

I expect most people to be dead within a few weeks. Those who are not, will be too busy with surviving to not have time to track around the globe searching for another survivor.

@Abigail I was just about to comment on that XD Not only are many climates too harsh for the inexperienced to survive without training/modern comforts, but also there is sickness (even a simple infected cut can be lethal without antibiotics), not to mention wild animals such as tigers in populous places like India.

What is particularly magic or special about the number 35 that was chosen?

Have things like the internet been wiped out? It obviously wouldn't last long with no one to look after it, but if everyone around me disappeared/died, I'd probably try making contact online... I'd even risk asking an off-topic question on SO/SE! (Probably only to find that one of the 34 other people was a moderator and see it closed :-( )

You may find the film 'The Quiet Earth' ineteresting. "A man wakes up to find himself literally alone in the world, and goes about trying to find other survivors, as well as to find out what happened."

@TripeHound You'd find that in the absence of moderation, spambots will make it all but impossible to use any website where users can contribute. Your post will be swamped in all the automated posts.

@Shadowzee but two of them will probably have the same birthday 🎂

I guess it would be safe to assume that every survivor would use all means possible to find someone else.

This question is entirely too broad and there is no way to provide a definitive answer. Please check out how to ask for more details on what should be included in a question.

@James I entirely disagree, since I think Drazex answered it very well.

@Eulb Suggestions for improving the question: 1) How "random" is it, really? Can it be any age? Is probability based on population or is it random locations? Are people with certain skills more likely to survive (like people with bunkers or outdoors skills)? 2) What infrastructure is in place? Any magic or alternate universe stuff? What time period? 3) Are survivors trying to find each other or are they focused on surviving in the aftermath? 4) What else is out there and why is everyone gone? Are there still animals? Is there radiation to deal with?

You don't necessarily need all of that information, but the more you can give, the better answer you will get.

@kingledion I don't disagree that it is a good answer but the question "When will two people run into each other" based on only a fixed number of people with no other information or guidance is too broad. The answer could be, immediately or never or any frame of time in-between and all answers would technically be correct. The querant is asking us to set the scenario which is part of the story, not building the world.

@Eulb No need to apologize, particularly since you are new to the site. Your question isn't bad, I just don't believe it is a good fit for the site, SE is a little different from standard forums/discussion boards. Its all about asking specific questions and getting specific answers. Check out the help center and tour to get a good idea of how the site works.

@Eulb I am not sure this question can or should be changed at this point. 1. We already have 12 answers, any functional changes to the question would likely invalidate the existing answers which is frowned upon. 2. At its core the question asks about what boils down to a story point. "How likely are two people to run into each other" depends on a thousand (give or take) variables and good old chance. I am not sure there is a way to make this question on topic but I will think on it and let you know if I come up with anything.

I wonder what the likelihood is that any of the 35 people will be pregnant.