The magic number...

With my job heavily reliant on stats and working in a lotto friendly state, I never fail to get the joking question..."What's my chance of winning the lottery?" Well today, I decided to once and for all but a number on it.

I chose to go with a pick 6 example, as that is the query I was asked to solve. In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply.

So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.

1/50 × 1/49 × 1/48 × 1/47 × 1/46 × 1/45 = 1/11,441,304,000 So, at this point, your odds of winning are 1 in 11441304000. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 6 numbers can be written down, which for 6 numbers is 6! (6 factorial) or 720. Divide 11,441,304,000 by 720 to account for this, to get 15,890,700.

In other words, there are 720 different ways that the 6 numbers you choose can be filled out on your lottery ticket--if you choose your 6 numbers correctly, any of these ways will make a winning ticket. *Not good enough of a chance for me to play though.