Probability Rules

Addition, complement and multiplication rules.

P (A \cup B) = P (A) + P (B) - P (A \cap B), P (A^{'}) = 1 - P (A)

Variables

For independent events $P (A \cap B) = P (A) P (B)$ . Subtracting the intersection avoids double counting outcomes in both events.

$P (A) = 0.5, P (B) = 0.3$ independent: $P (A \cup B) = 0.65$ .

Probability of two independent events: intersection, union, complement, exactly one and neither.

Binomial Probability

Probability of exactly k successes in n independent trials.