The card will be either an ace or not an ace . These are mutually exclusive outcomes.
Recall from Example 1 a standard deck has 4 suits (hearts, diamonds, clubs, and spades). Each suit has an ace; therefore, there are 4 aces in the deck. The probability of an ace occurring is
The probability of not drawing an ace from a standard deck is
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or about 92%.
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Watch the
Combining Probabilities
video to see examples using a probability tree diagram to solve problems involving mutually exclusive events including complementary.
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At the beginning of this Training Camp , you learned that not all events are mutually exclusive. Some events share outcomes. These events are called non-mutually exclusive events.
For any two non-mutually exclusive events, the probability that event A or event B will occur is given by the formula:
Written in set notation, the formula is
If two events are non-mutually exclusive, their outcomes intersect. Therefore, you must subtract outcomes that are in the intersection so that they are not counted twice. In the formula, this is shown as
or
.
Example 5 illustrates how to use this formula.