Friday, June 3, 2011

The math behind the lotto 649

In my Math 30 Applied Class, we had to cover probability.  Instead of using context questions around dice, spinners, and marbles, I allowed students to research any topic they found interesting around probability.  I would like to show you: "The math behind the Lotto 649" by Christine, one of my students.

Many people in the world play the lottery each year. You might believe in faith, chance or luck but I believe in math.  As you already may know, the chances of winning Lotto 6 49 is not very likely. So why do people play? I can’t really answer that question but for those who are sceptical I can convince you on why you shouldn’t play.
The probability of winning the Lotto 6 49 is 1 out of 13,983,816. The probability of losing the Lotto is 13,983,815 out of 13,983,816.
I’m going to make a scenario about a man named Dave who started playing 6 49 at the age of 18 until he was 80 years old. He bought a ticket twice a week. Each ticket consists of two rows, so technically he is playing four times a week. What is the probability of Dave not winning in his life?
Dave played the lotto for 62 years in his life.
There is 52 weeks in a year.
4/week x 52/year x 62 years = 12896
The total amount of times Dave played is 12896.
13983815/13983816 = 0.9999999999999…..
0.99999999999……^12896 = 99.9%
The reason why you shouldn’t play the Lotto 6 49 is that the chance of you not winning is 99.9% in your life time.
How much money would you spend on buying the tickets?
Each line is 2 dollars and you played 12896 which is 25792$.


  1. This is wrong because you get a bonus number, right idea though!

  2. Also numbers have decend so it would be 49*48*47*46*45*44 = 10068347520.00, lol good luck!

    1. 49*48*47*46*45*44=49P6 implies that order matters. 49C6 is the correct approach since order doesn't matter with the lottery