# How do you add probabilities?

Dec 3, 2017

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

#### Explanation:

Suppose A and B are two events.

$\setminus P \left(A \setminus \textrm{\mathmr{and}} B \setminus \textrm{o \mathcal{u} r s}\right)$ = $P \left(A \setminus \cup B\right) = P \left(A\right) + P \left(B\right) + P \left(A \setminus \cap B\right)$

Here $P \left(A \setminus \cap B\right)$ is the probability that the two events occur simultaneously. If these events are disjoint, $P \left(A \setminus \cap B\right) = 0$ 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 $P \left(A \setminus \cup B\right) = 0.1 + 0.2 = 0.3$