Glossary
Addition Rule (General Addition Rule)
The general addition rule calculates the probability of the union of two events A and B: P(A or B) = P(A) + P(B) - P(A and B). The subtraction accounts for outcomes counted twice.
Example:
If 60% of students like pizza (P) and 40% like tacos (T), and 20% like both, the probability that a student likes pizza or tacos is P(P) + P(T) - P(P and T) = 0.60 + 0.40 - 0.20 = 0.80, using the Addition Rule.
Conditional Probability (as it relates to independence)
For independent events A and B, the conditional probability of A given B is simply the probability of A, P(A|B) = P(A), because B provides no new information about A.
Example:
If the probability of a student getting an A on a pop quiz is 0.2, and whether they ate breakfast is independent of their quiz score, then the conditional probability of getting an A given they ate breakfast is still 0.2.
Dependent events
Two events are dependent if the occurrence of one event changes the probability of the other event occurring. Their outcomes influence each other.
Example:
The probability of needing an umbrella is dependent on whether it is raining outside.
Independent events
Two events are independent if the occurrence of one does not affect the probability of the other occurring. They have no influence on each other.
Example:
When you roll a standard die, the outcome of the first roll (e.g., getting a 6) is independent of the outcome of the second roll.
Multiplication Rule (for independent events)
If events A and B are independent, the probability that both A and B will occur is the product of their individual probabilities: P(A and B) = P(A) * P(B).
Example:
If the probability of passing your math test is 0.8 and the probability of passing your history test is 0.9, and these are independent events, the probability of passing both is 0.8 * 0.9 = 0.72, using the Multiplication Rule.
Mutually exclusive events
Two events are mutually exclusive (or disjoint) if they cannot occur at the same time. They have no outcomes in common.
Example:
When drawing a single card from a deck, the event of drawing a heart and the event of drawing a spade are mutually exclusive events because a card cannot be both a heart and a spade simultaneously.
Union (of events)
The union of two events A and B, denoted A ∪ B, is the event that A occurs, or B occurs, or both occur. It represents 'A or B'.
Example:
If event A is 'getting an A in Stats' and event B is 'getting an A in English,' the union (A ∪ B) is the event of getting an A in Stats, or an A in English, or both.