Finding Probability of a falling fan In a certain interview this question was asked to one of my friends by the interviewer 

what is the probability of this running fan (pointing at a ceiling fan) to fall down?

Actually to find the answer I feel that sample space is two

a. Either the fan will stay at its position.
b. Or The fan will fall down.
 So what I feel, probability is 50% 
Please let me know whether this is true or false, guide me for the thinking. I'm also going to sit for similar kind of interview. Please help 
 A: A distribution need not be uniform. The sample space for the sum of two dice is 11: $\{2,3,4,5,6,7,8,9,10,11,12\}$, but $2$ and $12$ can only happen a single way, whereas there are six ways a $7$ can be rolled.
Of course, most likely this question has no right answer, because it is an "interview 2.0" question.
However, if you actually were being hired as a reliability engineer for ceiling fan mounts, the appropriate answer is that you would have to perform a maximum likelihood analysis using right-censored data: since you don't know the time-to-failure of fans that have not yet failed, it is impossible to completely describe the distribution. Instead, we must make some assumptions on the tail distribution of the right tail of failure times and proceed from there.
A: You have several answers available to you:


*

*I have never seen this model of fan mount fail.  My prior expectation of failure is near zero and only deviates from zero because I am willing to entertain the notion that this mount or its installation is somehow at variance with my prior experience.  (This is a Bayesian argument.)

*(Your 50% is workable, but not the way you used it.)  The Copernican Argument is that there is nothing special about the time you have observed the fan.  Since it has not fallen during the past (however long you have been in the room, say 20 minutes, but use whatever your estimate of the real amount of time is) I predict with 50% confidence from the data so far that it will not fall in the next 20 minutes.  (The idea is that your observation has no special place in the history of the object (just as the Earth is not at a special place: the center of the universe) so you are equally likely to be observing it anywhere along that duration.)  If I knew that it had been mounted continuously for time prior to my presence in the room, I would adjust my estimate accordingly.

*100%.  Nothing lasts forever.  (This, depending on your outlook on like is either the optimistic, pessimistic, or realist position.)

*There are more ways to go, but this sort of question is just to see how much of a deer in the headlights response you produce.  Just don't let your brain seize up when something unexpected happens, as that might indicate a problem.

