Question: Let (A, B), and (C) be 3 arbitrary random events. (1) Express the event ' (A) occurs, but (B) and (C) do not occur' in

Let \(A, B\), and \(C\) be 3 arbitrary random events.

(1) Express the event ' \(A\) occurs, but \(B\) and \(C\) do not occur' in terms of suitable relations between these events and their complements.

(2) Prove: the probability of the event 'exactly one of the events \(A, B\), or \(C\) occurs' is

\[P(A)+P(B)+P(C)-2 P(A \cap B)-2 P(A \cap C)-2 P(B \cap C)+3 P(A \cap B \cap C)\]

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