The sample space is the set of every outcome of the lane draw, and an event is a set of those outcomes: "or" joins two sets, "and" keeps the overlap, "not" takes everything else. The addition rule P(A or B) = P(A) + P(B) - P(A and B) counts the overlap once. The conditional probability P(A given B) is the fraction of B's outcomes that are also in A, which is P(A and B) ÷ P(B). Two events are independent when P(A and B) = P(A) × P(B), the same as saying P(A given B) = P(A).