What would be more fun than winning the lottery? What if we can use math to win at the lottery? Suddenly math is fun! This article is a math primer to make winners. Even if you’re already good a math, there’s some fun facts that you might not have known before.
To begin, there are two things you need to know: how to calculate simple probability (to win), and scientific notation (to make life easier).
Probability
I Googled “probability to win mega millions” and the first hit was this article from CNBC.
Since Mega Millions modified the formula, players now pick five numbers from 1 to 70 and a Mega number of 1 to 25. The odds of winning the jackpot are now 1 in 302,575,350, the Post reported.
Evidently that number is hard to calculate right? After all, CNBC got the number from the Post who got it from who knows where? Perhaps those immortal mathematicians behind the curtain. Sorry, it’s not that difficult. You’ll probably need a calculator, but here’s how it’s done: Your first step in playing the lottery is to select your first number. What’s the probability that you get one of those 5 winning numbers? You have 5 in 70 chance. That’s 70÷5 = 14; and stated as a 1 in 14 chance of your first selection being one of the winning numbers. That’s not so hard!
Now for the next number. If you won the first number, there are 4 left in the pile of 69. So, you have 4 in 69 chance (69÷4 =17.25 or 1 in about 17) of getting the second number AFTER you already got the first number. To figure out probability you just multiply the probabilities of the individual events (in this case picking 5 numbers, then picking that mega number (1 chance in 25). Here’s the result:
There’s that enormous number which they want you to forget every time you donate $2 to the scammers. Why do they want you to forget it? If you don’t think about this number, and keep listening to the advertising, you’ll play (pay) the fool’s game. I find it amazing that governments once banned this type of exploitation of the poor, ignorant, and needy; but now they embrace it. I can afford $2 to play many times over. But I refuse to play even once because of the damage this ultimate tax-the-poor scam is doing to our society. (Sorry, I digress!)
For the genius out there: Yes, I know my ratios are upside down, probability is a number less than 1, and the probability is actually 1÷302,575,350 = 0.0000000033.
Scientific Notation
If we’re going to talk science, we need to use numbers. Numbers in science get very large (like the number of atoms in the human body), or very small (like the size of an atom). Both cases require a lot of zeros before the decimal point (large numbers) or after the decimal point (small numbers). Like everyone, we’re lazy and don’t like writing them out so many times. Next time, instead of writing one hundred million like this — 100,000,000 – write it like this 1×108. That “108” is just 10×10×10×10×10×10×10×10 (10 multiplied by itself 8 times). More simply, just think of the “8” which is called the exponent as moving the decimal point to the right 8 times. If there isn’t a decimal point, then add a zero. If the exponent were “-8” we’d move the decimal to the left, making the number very small and have 0.00000001 (one ten billionth).
So how do we write that probability number we calculated? Move the decimal 8 times to the left (reverse from before because we’re adding the notation, not taking it away) and add “×108” which looks like this 3.02575350×108. But that’s not any better!
Once again laziness comes to the rescue! We like to round (approximate). When you have such a large number (302,575,350), why worry about the last 50? Even 575 thousand is insignificant when compared to 302 million! What about the 2 million. That might be considered as insignificant too. The important part of the number is just the 300 million. You have 1 in 300 million chance to win Mega Fools Millions. Using scientific notation, this is expressed as 3.02×108, or rounding more to 3×108.
Now for something very interesting that perhaps most scientists haven’t considered!
George Washington died March 4, 1797. He breathed his last on that day and died – a great man. Assuming that in the 200+ years since his death those molecules have had the opportunity to disperse completely across the whole earth (pretty reasonable assumption given wind currents and such), let’s see how many breaths you have to take to be able to say, “I’ve breathed some of the same molecules that George Washington breathed on his very last breath.” To get this answer, we need some data:
Number of molecules in a breath: 1.25×1022
Number of molecules in Earth’s atmosphere: 1.09×1044
Now let’s use both probability and scientific notation. The probability of the first molecule of your next breath being one of George Washington’s last is the ratio of these two numbers.
That’s 1 chance in 87 with 20 zeros! That’s a really small chance, but that’s only the first molecule of your next breath. You still have 1.25×1022 more to go (minus that first one). Each molecule you breath in has approximately the same probability (we don’t have to subtract the numbers like we did when calculating lottery odds, although we can if we want to). So the simple equation is this:
Or otherwise stated a chance of 1 in 1. That is, odds are that your next breath will have one molecule from George Washington’s last breath. Some breaths will have zero, others 2 or 3, but odds are, each breath has about one. So good luck trying to avoid your neighbors sneezing and coughing!
Disclaimer: I did leave out an important factor – the air molecules continually are interacting with the trees, oceans, and earth which complicates things a bit. So the last-breath odds are less than 1 in 1, but are still very good and it’s accurate to say that molecules (or atoms) from George Washington’s last breath are all around us and we’re constantly breathing them every minute of every day.
The title suggests that I’m going to tell you the fool-proof numbers to play to win the lottery. I’m sure you already know, but here they are anyway: zero, zero, zero. Play zero times today, zero times tomorrow, and zero times the rest of your life. You’ll win every time you don’t pay.
Now it’s time to go here and uncover the greatest lottery scam of all time.
