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An event may result in A, B or C.

The probability that the result is A or B is 96.1%
The probability that the result is A or C is 84.0%
The probability that the result is B or C is 33.3%

What is the probability for A, B and C? Is it even possible to calculate given the above statements?

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up vote 2 down vote accepted

It would be possible to solve if no more than one of A, B and C can be true at a time: you would solve three simultaneous equations for the three unknown individual probabilities.

But that cannot be the case here as summing the three percentages comes to over 200% (in fact to 213.4%). So the sum of the three individual probabilities must be over 100%, and it must be possible for a number of the events to happen at the same time. You need to know more information to get the individual probabilities of each event.

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