# How do you add probabilities?

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oldgaffer1b
We can add two probabilities as long as the events are disjoint.

Explanation:
Suppose A and B are two events.
$P\left(A\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}B\phantom{\rule{1ex}{0ex}}\text{occurs}\right)$=$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)+P\left(A\cap B\right)$
Here $P\left(A\cap B\right)$ is the probability that the two events occur simultaneously. If these events are disjoint, $P\left(A\cap B\right)=0$ and in that case we can add the probabilities.
For example: Suppose events A and B are disjoint, $P\left(A\right)=0.1,P\left(B\right)=0.2$, then $P\left(A\cup B\right)=0.1+0.2=0.3$