What are your chances of winning? A quick look at the Powerball website tells you that the probability of winning the jackpot is 1 in 175,223,510. To see where that number comes from, imagine buying each number combination. In Powerball, a player first chooses five different whole numbers between 1 and 59. One could make a list of all possibilities, starting with (1, 2, 3, 4, 5), (1, 2, 3, 4, 6 ), and so on until the end (55, 56, 57, 58, 59). But it would take a long time to make that list, because it has more than five million entries! In fact, mathematics tells us that the number of ways to choose five different numbers from 1 to 59 is 5,006,386.
After choosing the five numbers between 1 and 59, the player chooses another number between 1 and 35 called Powerball. So, we multiply the 5,006,386 by 35 and we see that there are 175,223,510 possible Powerball combinations. To simplify, let’s be generous and round to 175,000,000.
Your chance to win the lottery on an individual ticket is one in 175 million. That seems small, and it is. In fact, it is so small that it is difficult for us to understand. Understanding how small this number is provides the key to understanding how likely or unlikely it is that 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 more chances of being struck by lightning,” we say often. But that does not provide much basis for comparison. We realize that being hit by lightning is unlikely, but we have no idea how unlikely it is, and of course the possibility of being struck by lightning is very different for a farmer than a coal miner.
The problem of catching the smallness of “1 in 175 million” is that we never see 175 million different objects. It is easy to capture 1 in 50, for example, because we can imagine with 49 other people in a room. We can concentrate on 1 in 75,000 (approximately) by visualizing the crowd in the Super Bowl and imagining ourselves as the only person selected from that crowd to win a prize. But one in 175 million can not be easily visualized.
This is an example I’ve used in classrooms across the country, and it’s much more fun than thinking about being struck by lightning! Imagine that 175 million freshly minted dollar bills are delivered to my home near Washington, DC One of those dollar bills is marked especially as the “lucky dollar bill”. You can choose a dollar bill, and if you choose the lucky dollar bill, you win all the dollar bills.
A simple mathematical calculation using the dimensions of a dollar bill reveals that it will take two semi-trailers to deliver the 175,000,000-dollar bills to my house. Once they arrive, they will have to be downloaded, of course, so you will have a good chance of choosing the lucky one dollar bill. Therefore, we will establish them end-to-end. How long will that line of dollar bills last?
If we start from my house, we will have enough dollar bills to go to Disney World in Orlando. Then we’ll still have enough to go all over the country to Disneyland! But, even then, we do not have dollar bills left, so we can go north and get to Portland, Oregon. Still, we have dollar bills, enough to get to Portland, Maine. And, fortunately, we will have enough to return to my home near DC, completing the cycle.
Do we have dollar bills? Yes! We would still have enough one dollar bills to travel the entire circuit for the second time!
Now imagine that you walk, bike or drive as long as you want in the double circuit, and when you decide to stop, you lean over and pick up a dollar bill. Your chance to select the lucky dollar bill is one in 175 million, as well as your chance to win the Powerball jackpot!
Your chance to win this great prize is incredibly small. It’s not going to happen. But you could say, “If the chances of winning are so small, how did Mark and Cindy Hill win?” Or put another way, “If you can do it, why can not I?” I will explain that in a future publication.
It is not my purpose or place to discourage people from buying lottery tickets. I just want everyone to understand their possibilities in the most complete and accurate way possible.