LOTTERIES:

One way of charactering such problems  is to use  the concept of a lottery. A lottery represents a pair of objects. First, Xi  is a list of possible consequences of a decision and second is a list P = (P₁,  P₂  .... P_n)  of  probabilities with which we  think  of  the  occurances  of  each  consequence.  Note that  the  number  of probabilities is equal to the number of consequences in X. Each of the consequences could  be  a  lottery. Thus,  if X = {X₁,  X₂ ...  X_n)  be  the  space of constituted of all possible states of events and P  = {p_l,  p₂,  ...  p_N}  is a probability distribution,  then we call the pair L = {X; P = X₁, X₂,  .. X_n;  p₁, p₂,  ... P_n}  a lottery.  

Simple Lottery

Simple lottery  L  is  a  list  L  = (P₁,  P₂  .... P_n)  with  p_n ≥ 0  for  all  n and ∑p_n =  1 where p_n  is the probability of outcome n occurring. 

Example

You  purchased a lottery  ticket.  The set of  consequences consists  of  two elements: you  either win or lose a prize. You  also know  that each of these consequences occurs with probability 1/2.