Question

How do you add probabilities?

Answer 1

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

Explanation:

Suppose A and B are two events.

`\P(A \text{ or } B \text{ occurs})` = `P(A \cup B) = P(A) + P(B) + P(A \cap B)`

Here `P(A \cap B)` is the probability that the two events occur simultaneously. If these events are disjoint, `P(A\cap B)=0` and in that case we can add the probabilities.

For example: Suppose events `A` and `B` are disjoint, `P(A) = 0.1, P(B) = 0.2`, then `P(A \cup B) = 0.1 + 0.2 = 0.3`