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numbers and algebraic expressions
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combinatorics
probability
elements of statistics
kropki game

S - the set of all equally likely outcomes. The probability is any function P which assigns to each event A ⊂ S a real number P(A) and satisfies the following axioms: P(A) ≤ 0, P(S) = 1, if A ∩ B = ∅ then P(A∪B) = P(A) + P(B). Properties of probability. If P is the probability, given on the subsets of S, then for any event A, B ⊂ S the following properties are true: P(∅) = 0, P(A) ≤ 1, if A ⊂ B then P(A) ≤ P(B). If A and A' are complementary events then P(A') = 1 - P(A), P(A∪B) = P(A) + P(B) - P(A∩B).