Probability

Addition Rule for Disjoint Events
P(A \text{ or } B) = P(A) + P(B)
General Addition Rule
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
Complement
If set S = {1,2,3} and D = {1}
Then the complement is: D^c = {2,3}
Multiplication Rule for Independent Events
P(A \text{ and } B) = P(A) \times P(B)
Conditional Probability
P(A|B) = \frac{P(A \text{ and } B)}{P(B)}
General Multiplication Rule
P(A \text{ and } B) = P(A|B) \times P(B)
Bayes' Theorem
P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}
Independence Rule
P(A \text{ and } B) = P(A) \times P(B)
Independence Rule
P(A|B) = P(A) \text{ and } P(B|A) = P(B)