Is probability determined by perspective? My question: is probability determined by perspective?  
The scenario that raised the question for me: 
Initial condition: The Monty Hall problem.  We know the contestant’s original choice of door #1 (of 3 total) is only correct 33% of the time.  After Monty Hall reveals door #3 is incorrect the contestant is asked if he would like to switch his answer to door #2.  We know he should choose to change his answer to the other unopened door (#2) which has a 66% chance of being correct.  He does so.  
However, let’s say once he decided to switch to door #2, and before either door is revealed, another contestant enters the room.  She does not have any knowledge of what has just transpired on stage.  She is offered a choice to pick which door the car behind of the 2 remains closed doors and also randomly chooses door #2.  
Are the probabilities of being correct different for each contestant?  Seemingly they are.  Contestant 1 had 3 doors to choose from, giving him a probability of 33% that door #1 is the answer.  Contestant 2 only had 2 doors to choose from, giving her a probability of 50% after choosing the same door contestant #1 choose.  
If we repeat the experiment 1000 times, what will the numbers turn out to be for door #1?  333 or 500?


Is probability determined by perspective?

The answer is undoubtedly yes, but I don't think the Monty Hall problem illustrates the possibility of different perspectives well. Rather I like Bertrand's Paradox.

Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?   

Bertrand then gave three answers depending on different probability distributions. The whole point was that for the problem to have a particular solution then the probability distribution for the chord length distribution must be specified in the problem statement since different distributions lead to different answers. 
