Intersection

Definition

The intersection of two events in probability is the set of outcomes that are common to both events. It is denoted by $A \cap B$.

5 Must Know Facts For Your Next Test

1. The intersection of events $A$ and $B$, written as $A \cap B$, represents the outcomes that both events share.
2. If events $A$ and $B$ are mutually exclusive, then $A \cap B = \emptyset$, which means their intersection is empty.
3. The probability of the intersection of two independent events $A$ and $B$ is given by $P(A \cap B) = P(A) \cdot P(B)$.
4. For dependent events, the probability of their intersection can be found using conditional probability: $P(A \cap B) = P(A) \cdot P(B|A)$.
5. In a Venn diagram, the intersection of two sets is represented by the overlapping region between the circles representing each set.

Review Questions

• What does the notation $A \cap B$ signify in probability?
• How do you calculate the probability of the intersection for two independent events?
• What is true about the intersection of two mutually exclusive events?

Related terms

Union:

The union of two events includes all outcomes that belong to either event or both, denoted as $A \cup B$.

Mutually Exclusive: Two events are mutually exclusive if they cannot occur at the same time, meaning $A \cap B = \emptyset$.

Conditional Probability:

The probability of an event occurring given that another event has already occurred, represented as $P(B|A)$.