Addition Rule in Probability

If A and B are two events in a probability experiment, then the probability that either one of the events will occur is:

P(A or B) = P(A) + P(B) – P(A and B)

This can be represented in a Venn diagram as:

If A and B are two mutually exclusive events , . Then the probability that either one of the events will occur is: P(A or B) = P(A) + P(B). .

This can be represented in a Venn diagram as:

Example:

If you take out a single card from a regular pack of cards, what is probability that the card is either an ace or spade?

Let X be the event of picking an ace and Y be the event of picking a spade.

The two events are not mutually exclusive, as there is one favorable outcome in which the card can be both an ace and spade.