Probability question I can't work out

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The discussion centers on solving a conditional probability problem involving events A and B, where event C occurs if exactly one of A or B occurs. The correct formula to derive is Pr(C) = Pr(A) + Pr(B) - 2Pr(A ∩ B). The user suggests that C can be expressed as the union of mutually exclusive events (A-B) and (B-A), leading to the evaluation of probabilities to confirm the result. This approach utilizes basic probability axioms and set-theoretic principles.

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Hey

I've just joined here and I'm doing some revision on conditional probability. This one question, which I know should be simple, has me stumped. I've tried what I can think of but I can't seem to get it right. Any help anyone may have would be very much appreciated.

Suppose A and B are events and de ne the new event C to occur if and only if
exactly one of A or B occur. Show algebraically, using only the probability axioms and
properties, and basic set-theoretic results given in the lectures, that
Pr(C) = Pr(A) + Pr(B) - 2Pr(A n B)

Thank you
 
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C=(A-B) or (B-A), which are mutually exclusive events.. Evaluate probabilities to get result.
 

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