Thus, suppose that the player's selected combination Y is a random variable taking values in S . In the following exercise, you will show that such randomization makes no difference. Let U denote the number of catches in the N , n , m lottery when the player's combination Y is a random variable, independent of the winning combination X . Show that U has the same distribution as in Exercise 1. There are many web sites that publish data on the frequency of occurrence of numbers in various state lotteries.
Some gamblers evidently feel that some numbers are luckier than others.
The prize money in most state lotteries depends on the sales of the lottery tickets. The total prize money is divided among the winning tickets, and the prize for a given ticket depends on the number of catches U . For all of these reasons, it is impossible to give a simple mathematical analysis of the expected value of playing a given state lottery. Note however, that since the state keeps a fixed percentage of the sales, there is essentially no risk for the state. From a pure gambling point of view, state lotteries are bad games.