Winning Powerball Lottery // Lotteries

Winning Powerball Lottery

In November 2012, a Missouri couple and an Arizona man shared the largest Powerball jackpot ever - $587 million. An article about the Missouri couple - Mark and Cindy Hill - appeared in The Huffington Post on February 25 telling a wonderful story about how the couple is using their winnings to benefit their community. Such stories lead us to daydream about what we might do if we won all that money.

What are your chances of winning? A quick look at the Powerball website tells you the probability of winning the jackpot is 1 in 175, 223, 510. To see where that number comes from, imagine purchasing every number combination. In Powerball, a player first picks five different whole numbers between 1 and 59. One could make a list of all the possibilities, starting with (1, 2, 3, 4, 5), (1, 2, 3, 4, 6), and so on all the way through (55, 56, 57, 58, 59). But it would take a long time to make that list, because it has more than five million entries! Indeed, mathematics tells us the number of ways to choose five distinct numbers from 1 to 59 is 5, 006, 386.

After choosing the five numbers between 1 and 59, the player then picks another number between 1 and 35 that is called the Powerball. So, we multiply the 5, 006, 386 by 35 and see that there are 175, 223, 510 possible Powerball combinations. For simplicity, let's be generous and round off to an even 175, 000, 000.

Your chance of winning the lottery on a single ticket is one in 175 million. That seems tiny, and it is. In fact, it is so small that it is difficult for us to grasp. Understanding how small this number is provides the key to understanding how likely - or unlikely - it is you will become the next big winner of the Powerball jackpot.

For some reason, we tend to associate unlikely events with a specific physical phenomenon. "I have a better chance of being struck by lightning, " we often say. But that does not provide much of a basis for comparison. We realize being struck by lightning is unlikely, but we have no sense of how unlikely, and of course the chance of being struck by lightning is much different for a farmer than a coal miner.

The problem with grasping the smallness of "1 in 175 million" is that we never see 175 million distinct objects. It is easy to grasp 1 in 50, for example, because we can imagine ourselves with 49 other people in a room. We can get our minds around 1 in 75, 000 (roughly) by visualizing the crowd of people at the Super Bowl and imagining ourselves being the one person selected from that crowd to win a prize. But one in 175 million cannot be readily visualized.

Here is an example I have used in classrooms all over the country, and it is way more fun than thinking about being struck by lightning! Imagine 175 million freshly minted one-dollar bills are being delivered to my house near Washington, D.C. One of those dollar bills is specially marked as the "lucky dollar bill." You get to pick a dollar bill, and if you happen to pick the lucky dollar bill, you win all the dollar bills.

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Popular Q&A

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What are the winning Powerball lottery numbers?

The winning Powerball numbers from April 4, 2009, are 14 21 50 57 58 and 7. Thanks for using today!


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