Classical Probability
P(A) = |A| / |S|
Favorable outcomes ÷ Total equally likely outcomes
Complement Rule
P(A') = 1 − P(A)
Probability of event NOT occurring
Addition Rule
P(A∪B) = P(A)+P(B)−P(A∩B)
For mutually exclusive: P(A∩B) = 0
Conditional Probability
P(A|B) = P(A∩B) / P(B)
Probability of A given B has occurred
Independence
P(A∩B) = P(A)·P(B)
A and B independent if P(A|B) = P(A)
Bayes' Theorem
P(A|B) = P(B|A)·P(A)/P(B)
Reverse conditional probability
Binomial Distribution
P(X=k) = C(n,k)·p^k·(1−p)^(n−k)
n trials, k successes, prob p each
Expected Value
E(X) = Σ x·P(X=x)
Long-run average; Binomial: E(X)=np
Combinations
C(n,r) = n! / (r!(n−r)!)
Order does NOT matter
Permutations
P(n,r) = n! / (n−r)!
Order DOES matter