Key rules to internalize:

P(not A) = 1 - P(A) — the complement rule - P(A or B) = P(A) + P(B) - P(A and B) — the addition rule - P(A and B) = P(A) × P(B|A) — the multiplication rule - P(B|A) = P(A and B) / P(A) — the definition of conditional probability