2. 4 PROBABILITY The classical or a priori definition if an experiment can result in n mutually exclusive and equally likely outcomes and if m of these outcomes are favorable to event a then P(A, the probability that A occurs, is m/n P(4)= the number of outcomes favorable to a the total number of outcomes Two features of the probability (1) The outcomes must be mutually exclusive: (2) Each outcome must have an equal chance of occurring
2.4 PROBABILITY • 1．The Classical or A Priori Definition：if an experiment can result in n mutually exclusive and equally likely outcomes, and if m of these outcomes are favorable to event A, then P(A), the probability that A occurs, is m/n Two features of the probability: （1）The outcomes must be mutually exclusive; （2）Each outcome must have an equal chance of occurring. the total number of outcomes the number of outcomes favorable to A ( ) = = n m P A
2. 4 PROBABILITY 2. Relative Frequency or Empirical Definition Frequency distribution how an r.v. are distributed Absolute frequencies: the number of occurrence of a gIven event. Relative frequencies: the absolute frequencies divided by the total number of occurrence Empirical Definition of Probability if in n trials (or observations), m of them are favorable to event then P(A), the probability of event A, is simply the ration m/n (that is, relative frequency) provided n, the number of trials, is sufficiently large In this definition we do not need to insist that the outcome be mutually exclusive and equally likely
2.4 PROBABILITY • 2.Relative Frequency or Empirical Definition Frequency distribution: how an r.v. are distributed. Absolute frequencies: the number of occurrence of a given event. Relative frequencies: the absolute frequencies divided by the total number of occurrence. Empirical Definition of Probability: if in n trials（or observations）, m of them are favorable to event A, then P（A）, the probability of event A, is simply the ration m/n, （that is, relative frequency）provided n, the number of trials, is sufficiently large In this definition, we do not need to insist that the outcome be mutually exclusive and equally likely
2.4 PROBABILITY 3. Properties of probabilities (1)0≤P(A)≤1 (2) If A, B, Cr.. are mutually exclusive events then P(A+B+C+.=P(A+P(B)+P(C)+ (3 If A, B, Cr.. are mutually exclusive and collectively exhaustive set of events, P(A+B+C+…)=R(A+P(B)+P(C)+.=1
2.4 PROBABILITY • 3. Properties of probabilities (1) 0≤P(A)≤1 (2) If A, B, C, ... are mutually exclusive events, then: P(A+B+C+...)=P(A)+P(B)+P(C)+... (3) If A, B, C, ... are mutually exclusive and collectively exhaustive set of events, P(A+B+C+...)=P(A)+P(B)+P(C)+...=1