Odds of impostor?

Question

Assume I left a hotel room key at the concierge to be picked up by my friend John Doe. The key is put in an envelop, "John Doe" is written on the outside of the envelop, and the people at the concierge will give the envelop containing the key to anyone asking for an envelop for John Doe.

How can I compute the odds that some impostor will come to the hotel's concierge asking for an envelop for John Doe? What assumptions must be made to compute the odds? Population of the city? Number of hotels in the city? Popularity of the name? Number of days in a year? Number of hours in a year? Can this even be computed?

Answer 1

I think this question is practically incomputable- that is, we can state assumptions that would allow us to address the question, but in reality the assumptions could never be expected to hold or even to control the premises, as the occurrence of an individual event is unlikely to conform to a trend, but instead to represent a severe outlier.

Let's imagine an (maximally) accurate long-term model producing a Poisson distribution of visitors to the front desk who ask for envelopes for "John Doe". This model may be able to correctly reflect the long-term probability, but in a single case, the following would have extremely more bearing on the possibility than anything that could be considered in the model realistically:

1. Are you being investigated/followed/stalked by anyone?
2. Are any of the hotel employees with access to the message involved in a criminal enterprise involving theft of customer goods?
3. Does anyone have a strong motivation to cause you harm or steal from you?
4. Have you kidnapped Liam Neeson's daughter and are holding her hostage in the room in question?

Point being, demographic values would be comparatively un-predictive to this premise as one unknown factor, which could easily raise the probability to 1.

Can you manufacture a model that would create a long-term trend of the example? Maybe, but it would be all but worthless for a single prediction.