Glossary
Addition Rule for Mutually Exclusive Events
For two mutually exclusive events A and B, the probability that A or B occurs is the sum of their individual probabilities: P(A or B) = P(A) + P(B).
Example:
If the probability of choosing a red marble is 0.3 and the probability of choosing a blue marble is 0.4 (and you can only choose one), then the probability of choosing a red or blue marble is 0.3 + 0.4 = 0.7, using the addition rule for mutually exclusive events.
Independent Events
Events where the occurrence of one event does not affect the probability of the other event occurring. They are distinct from mutually exclusive events.
Example:
Flipping a coin and getting heads, and then rolling a die and getting a 6, are independent events because the coin flip's outcome doesn't influence the die roll's outcome.
Intersection (Joint Probability)
The intersection of two events, A and B, is the probability that both events occur at the same time. It represents the outcomes common to both A and B.
Example:
The intersection of a student being on the honor roll and also playing a varsity sport is the probability that a student does both.
Mutually Exclusive Events
Events that cannot happen at the same time; they have no outcomes in common. If two events are mutually exclusive, their intersection probability is zero.
Example:
When rolling a standard six-sided die, rolling an even number (2, 4, 6) and rolling an odd number (1, 3, 5) are mutually exclusive events because you cannot roll a number that is both even and odd simultaneously.