List of formulas for the theorem of addition and multiplication of probabilities:
Probability addition theorem
- For two events A and B:
[
P(A \cup B) = P(A) + P(B) – P(A \cap B)
]
(where (P(A \cup B)) is the probability that at least one of the events A or B will occur, (P(A \cap B)) is the probability that both events will occur). - For two mutually exclusive events A and B:
[
P(A \cup B) = P(A) + P(B)
]
(if events A and B cannot occur simultaneously).
Probability Multiplication Theorem
- For two independent events A and B:
[
P(A \cap B) = P(A) \cdot P(B)
]
(where (P(A \cap B)) is the probability that both events A and B will occur). - For two dependent events A and B:
[
P(A \cap B) = P(A) \cdot P(B | A)
]
(where (P(B | A)) is the conditional probability of event B given that event A has occurred).