Feel the Power of Odds

The Powerball Jackpot this past Wednesday was topping $500,000,000.00. That’s five hundred million dollars. That’s a half of a billion dollars. Okay, now that we’ve established that this is a lot of money, what are your odds of winning it? According to the website, the odds are 1 in 175,223,510. That means that there are more 175 million combinations that possible to be drawn, but only one combination can be drawn. How do we arrive at that number? That’s where math comes in. I am going to show you how to calculate the odds for any lottery.

For this example, I am using the Powerball lottery since it’s the one that is so much in the news.

The Rules: The player picks 5 numbers out of a pool of 59 (white balls) and another number from a pool of 35 (red balls). The numbers do not have to be picked in any particular order.

Picking numbers: You may pick any five numbers and a Powerball number or you may have the Lottery terminal pick them for you.

The draw (the calculation):

There are two ways to perform this calculation, I will cover both since they have the same outcome.

The first ball to come out can be any of the 5 numbers that you picked. There are 59 balls in the hopper. So the odds that the first number will be one of ours is 5 in 59.

59 / 5

The next ball to be drawn can be any of the remaining 4 numbers, but now there are 58 balls left. The odds for that ball is 4 in 58.

58 / 4

Naturally, the next will be 3 in 57.

57 / 3

And so on…

56 / 2 and 55 / 1.

When you multiply all of these fractions together, we get…

(59 / 5) * (58 / 4) * (57 / 3) * (56 / 2) * (55 / 1) = 5,006,386

That means that we can have 5 million+ combinations possible, but that’s only for the white balls. What about the Powerball? We pick 1 number out of a pool of 35, so that would be…

(35 / 1) or just 35.

We then multiply that into answer for the white balls…

5,006,386 * 35 = 175,223,510

There you go. Your odds of winning are 1 in 175,223,510.

The other way to do this calculation:

(59*58*57*56*55*35)/(5*4*3*2*1*1) (naturally, the two ones make no bit of difference except to act as placeholders for the number of balls drawn).

Did you win? Well, there were a total of two jackpot winning tickets out of over a quarter billion sold. There were more than nine million winning tickets sold (prizes ranging from $4 to $2,000,000). Go back to my previous post and tell me how you would have spent that cash.