In the United States, total annual lottery sales have grown into the billions of dollars.
Lotteries also provide an excellent opportunity to use elementary financial mathematics, as well as some probability, in a context familiar to students. Most students do not have major financial decisions to make, so the principles of financial mathematics may seem far removed from their lives. However, most of them are familiar with the lottery and the topic readily engages them. The application of these mathematical concepts in the lottery is discussed in this paper.
In several USA states and Canada Provinces, the 6/49 lottery operates as an average lottery. To win the lottery grand prize the contestant needs to select all six numbers exactly as drawn in the weekly or monthly contest. This will be used as the model system for the computations in this paper.
Starting with a bag of 49 differently-numbered lottery balls, there is clearly a 1 in 49 chance of predicting the number of the first ball selected from the bag. Accordingly, there are 49 different ways of choosing that first number. When the draw comes to the second number, there are now only 48 balls left in the bag (because the balls already drawn are not returned to the bag), so there is now a 1 in 48 chance of predicting this number.
Thus, each of the 49 ways of choosing the first number has 48 different ways of choosing the second. ...