So I would like to know the probability of the following scenario to happen.

I am from India. Jane(say) is from Brazil. I moved to Canada to work four months ago and have been hopping from one airbnb to another. Jane moves from Brazil to Canada to study and happens to be in the room next to me in the same airbnb. Now Jane and I are really good friends. Before this event actually happened, what would have been the chances(probability) of this meeting to occur?

I can provide any other details if required. Not looking for an accurate answer, but at least an approximate one.

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    $\begingroup$ This would require massive amounts of assumptions, so many that it would hardly resemble the original question being asked. $\endgroup$ – JMoravitz Aug 29 '18 at 18:22
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    $\begingroup$ It depends on the probability of what, exactly. The probability of the person in the next room being Jane? The probability of the person in the next room being anyone you already know? The probability of encountering anyone you already know at any time during the entire trip? All of these are different probabilities. $\endgroup$ – Tanner Swett Aug 29 '18 at 18:27
  • $\begingroup$ @TannerSwett the probability of Jane meeting me in this part of the world at this bnb on this day $\endgroup$ – Procrastinating Programmer Aug 29 '18 at 18:42
  • $\begingroup$ @ProcrastinatingProgrammer Any question about probabilities of real events needs simplifications and assumptions. I could ask "what is the probability of me writing this comment" and could easily answer $100\%$ (because assuming a deterministic universe, it was bound to happen) or $50\%$ (because I was either going to write a comment or not) or $4\%$ (because I'm one of the $25$ people who've viewed this question). It's a very difficult question you're asking, as there is incomplete information. Are all countries equally likely? Are all hotel rooms equally likely? $\endgroup$ – Jam Aug 29 '18 at 19:13
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    $\begingroup$ @ProcrastinatingProgrammer Right, but can you see how all of the questions that are prerequisites for your question each lead to other questions or assumptions? What if Jane doesn't want to pick an Airbnb near the coast, or what if there are no flights to Canada? Or what if you lost your plane ticket? Without an appropriate model or set of assumptions, the question cannot be answered :) $\endgroup$ – Jam Aug 29 '18 at 19:29

I will try to answer the question I suspect is behind your question.

The probability of that sequence of coincidences if specified in advance of the observation that they happened is extremely small. Estimating it would require lots of assumptions I wouldn't even try to specify.

That's because you did not ask in advance of the event. In fact, rare things happen all the time. If by chance you shared your B&B with a tall red headed man from Norway with the same first name as your brother that would be surprising - you didn't know it would happen.

Think about the lottery: the chance that any particular ticket will win is miniscule - but some ticket will win. The owner of that ticket will feel singled out by fate - as you do about your meeting with Jane. But there are people all over the world sharing B&Bs with a particular other person who don't take notics.


OK so what I think you need is this:

1) The number of people in Canada. I am calling this 36.3 million.

2) The number of people you 'meet' in say a year. i.e. the number of people you end up hanging out with this closely (next door to each other in the same airbnb). This is going to be of the order of 10 right? Please feel free to supply a different number.

On this basis we are talking about a probability of $10/36,300,000$ which will be small: $2.75 \times 10^{-7}$.

But maybe it is not this simple. Maybe the two of you know the same sort of people, move in the same circles. If this is the case perhaps you need to reduce the population in which you are moving from $36,300,000$ to your social stratum. That is a question for you. It could be a million, $10$ million or perhaps a few hundred. You then divide the annual number of contacts by the number in your social stratum.

I am doing the analysis over a year but it could be over a decade (higher chances as it increases the numerator) or a trip.

  • $\begingroup$ what if we factored in the number of people moving from Brazil to Canada on a given date $\endgroup$ – Procrastinating Programmer Aug 29 '18 at 18:39
  • $\begingroup$ @Simon Why would you factor in the number of people already in Canada, when they're both visitors? That figure would be including permanent residents. $\endgroup$ – Jam Aug 29 '18 at 19:25
  • $\begingroup$ It seems to me that the question is about the universe from which people who might take a room in an airbnb might be drawn. Is it Citizen's of Canada, visitors to Canada, members of your 'social stratum' or some other subgroup? This is really an empirical question so as mathematicians, all we can do is list the options. $\endgroup$ – Simon Terrington Sep 1 '18 at 14:39

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