What does $P(A \triangle B)$ mean?
I know its a simple question but its hard to google these symbols. Anyways, anyone care to explain what $P(A \triangle B)$ means? I haven't seen this symbol before and I'm not sure on how to interpret it.
$\endgroup$ 02 Answers
$\begingroup$The triangle is almost certainly being used to for symmetric difference:
$$A\mathrel{\triangle}B=(A\setminus B)\cup(B\setminus A)=(A\cup B)\setminus(A\cap B)\;.$$
The $P$ might be the power set operator, in which case the whole thing is the set of all subsets of $A\mathrel{\triangle}B$:
$$P(A\mathrel{\triangle}B)=\{X:X\subseteq A\mathrel{\triangle}B\}.$$
However, a script $P$ is more often used for this purpose, and as has just been pointed out to me, you used the probability tag, so $P(A\mathrel{\triangle}B)$ is probably the probability assigned to the subset $A\mathrel{\triangle}B$ of your sample space.
$\endgroup$ 2 $\begingroup$As in other post, $A\bigtriangleup B$ is the symmetric difference of 2 sets. $P(A\bigtriangleup B)$ is the probability that at least one of $A$ and $B$ but not both happens, i.e. exactly one of $A$ and $B$ happens.
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