Addition Rule in Probability
If and are two events in a probability experiment, then the probability that either one of the events will occur is:
This can be represented in a Venn diagram as:
If and are two mutually exclusive events , . Then the probability that either one of the events will occur is:
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 be the event of picking an ace and 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.