- #1

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## Homework Statement

Let A and B be events. Show that [itex]A\bar{B} \cup B \bar{A}[/itex] is the event which exactly one of A and B occurs. Moreover,

[tex]P(A\bar{B}) \cup B \bar{A}) = P(A)+P(B)-2P(AB)[/tex]

## Homework Equations

## The Attempt at a Solution

First of all I think that the problem statement is ambiguous because they don't specify the order of operations. I think they mean[itex](A\bar{B}) \cup (B \bar{A})[/itex]

So, basically I was trying to prove this using only the property

[tex]P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]

but that failed. I don't know what else to do.