We start with discussion on uncertainty, probability, belief and expectation, then introduce the idea of contingent payoffs, a list of possibilities "if event A, the payoff B". Averaging out contingent payoffs with probability weighted averages. What does probability "mean"? - 3 interpretations of probability (the formalists, where probability is a mathematics, the frequentists, where probabilities count of indefinitely repeatable events, the subjectivists, where probability is a personal degree of belief)