Background
Most people have a poor understanding of probability. One major difficulty is in appreciating how unlikely simple events become when several independent outcomes must all line up. This is one reason that lotteries are popular: people overestimate their chances of winning.
Most state lotteries use 6 numbers. The probability of matching all 6 is 0.02 X 0.02 X 0.02 X 0.02 X 0.02 X 0.02 or 0.000000000064. This number is so small that it is difficult for people to grasp how unlikely it is.
Many lotteries do not allow repeated numbers. In this case, the probability of matching all 6 is 1/50 X 1/49 X 1/48 X 1/47 X 1/46 X 1/45 which is approximately 0.00000000000874.
In the demonstration below, the average state lottery is simulated to show exactly how unlikely it is that you will match all 6 numbers. In this simulation, you try to match 6 numbers between 1 and 50. You get a prize for matching 3 or more numbers. The simulation assumes there is 1 drawing per week, tickets cost $1, and that you purchase 1 ticket for each drawing.
It also shows you what would happen if you put the $1 away each week in an investment that earned you 5% compounded daily.
Instructions
Click once on this button and a new window will appear.
Decide whether you want to do a quick pick for each drawing (if so, click once on Multi Quick Picks), a single quick pick which is used for every drawing (click once on Quick Pick), or you can enter your own lucky numbers (keep them between 1 and 50). If you want to enter your own numbers, first click once in the appropriate box, and then type in your number.
It you match 6 out of 6, you win $1,000,000 (virtual, not real, dollars).
To begin, click once on "Play." The simulation picks a different random set of numbers for each drawing. The simulation also keeps track of the number of times you match 3, 4, 5, or 6 items. Finally, it conveniently tracks how many years have elapsed, and the total amount of money you have won or lost. The bottom, left-most box shows how much money you would have if you put $1 a week in a savings account that paid 5%.
As you watch the years roll by, notice how many times you match 3, 4, or 5 out of 6. You can click on "Stop" and re-run the simulation with different numbers or with different payoffs. You can see if picking your own numbers makes a difference.
