Decision Making using Game Theory: An introduction for managers

33An introduction to basic probability theorySPR. .s iP{s i } = p iFigure 3.1A sample space and probability of an event.An introduction to basic probability theoryThe fundamental concept in probability theory is the notion of aprobability space.IfS is a set of events called the sample space,S s 1 ,s 2 ,s 3 ,...,s i ,...,s n and P is a function that assigns to every subset s iPs i p i , such that:0 p i 1a real numberthen the ordered pair (S, P) is called the probability space and Ps i p iis called the probability of s i (see Figure 3.1).The probability function, P(s), has the following six properties:∑ p i 0, i∑ Σp i 1, from i 1ton∑ If A S, then PA Σp i , for all events s i A∑ P 0∑ PS 1∑ If the sample space, S, isinWnite, then P(s) isdeWned only on somesubset of S.A number of other concepts Xow from those given above, amongthem the idea of a random variable and its distribution function. Arandom variable, X, is a function mapping S onto the real numbers.