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Is There a Difference Between Odds and Probability?

Grammar Girl joins us to ask two grammar-related math questions. First, what does the word ‘and’ mean in a sentence about math? And second, is there a difference between odds and probability?

By
Jason Marshall, PhD,
November 2, 2013
Episode #108

For the last few years, Grammar Girl (aka, Mignon Fogarty) and I have been writing back and forth sharing with each other some great questions from our readers and listeners that bridge the gap between the worlds of grammar and math. For nearly as long, we’ve been talking about someday joining forces to form a wonderfully geeky dynamic duo so that we can answer all of these questions that live on the harrowing ledge between our worlds. Today, I’m happy to report that at long last that day has come. You can find Mignon’s answers to my math-inspired grammar questions in the latest Grammar Girl article, and keep on reading to see my answers to Mignon’s grammar-inspired math questions.

What Does ‘And’ Mean in a Sentence About Math?

Grammar Girl:

First, can you tell me what the word ‘and’ means in a sentence about math? Some people have written in thinking that it always implies a decimal point, and other people think it means addition, and other people think it means something else. So it’d be great if you could clarify what ‘and’ means in a sentence about math.

Math Dude:

I’ve seen at least a half-dozen variations of this question the past few years, so it’s safe to say that it’s a common one. The short answer is that the word ‘and’ does not imply a decimal point in a sentence about math. Instead, it implies addition. For example, look at the common ways that people say the current year: “twenty-twelve,” “two-thousand twelve,” “two-thousand and twelve.” They’re all correct, but the last one is interesting because it has an ‘and’ in it. What does this ‘and’ mean? Well, the phrase “two-thousand and twelve” is really just a way to describe the addition problem 2000 + 12 = 2012. So that ‘and’ means addition. And how about a rather famous example from history: “Four-score and seven years ago…” Since a score is 20 years, “four-score and seven years” is just (4 x 20) + 7 = 87 years. Again, the ‘and’ implies addition.

If you’re wondering where the mistaken belief that ‘and’ always implies a decimal-point comes from, you can blame it on fractions. For example, "two and one-half" or "two and five-tenths" are both fractions that are equal to 2.5—which, you’ll notice is a number that has a decimal point. However, even in this case, the ‘and’ isn't referring to the fraction or the decimal point. Instead, it’s again referring to the need to add. In other words, “two and one-half” is the same as 2 + 1/2…the ‘and’ implies addition!

What’s the Difference Between ‘Odds’ and ‘Probability’

Probability and odds do not mean the same thing.

Grammar Girl:

What’s the difference between probability and odds? Do they mean the same thing? Or are they different?

Math Dude:

That’s a great question—odds are definitely a bit confusing. Let me start off by saying that this topic of probability and odds is a big and extremely important one. And because of that, we’re going to dedicate a bunch of upcoming shows to diving in deep and really understanding these ideas. Given that, we’re not going to worry about understanding every last detail about probability and odds today. Instead, we’ll just focus on the big picture. With that in mind, the key thing to know today is that probability and odds both describe how likely it is that something will happen—but they do it in different ways. Which means that probability and odds do not mean the same thing (although we can convert from one to the other).

Without going into too much detail, probability is a number between 0 and 1 that tells you the fractional likelihood that something will happen. So a probability of 0 means there’s literally no chance of that thing happening, a probability of 0.5 means there’s a 50% chance, and a probability of 1 means that it’s certain to happen. As you can see, the idea of probability is relatively simple. But the idea of odds, on the other hand, is a bit more complicated…mostly because there’s more than one way to write them. The most common way is what’s called “bookmakers odds.” For example, 3-1 (pronounced “three to one”) odds of a horse winning a race mean that for every four races (the total of the two numbers in 3-1), the horse will lose three times (the first number in 3-1) and win once (the second number in 3-1).

If you think about it, you’ll see that this way of writing odds is opposite to how we express the likelihood of winning with probabilities. In other words, 3-1 bookmakers odds means that the chances of a win are 1/4 which is a 0.25 probability. So that means that high bookmakers odds have a low probability of winning (but give a high return on a bet) and vice versa. Since this is all kind of a pain to keep straight in your head, my advice is to keep things simple and always write likelihoods as probabilities. And then when you run into odds, all you have to remember is how they relate to probabilities.

Wrap Up

Okay, that’s all the math we have time for today. Thanks for the great grammar-inspired math questions, Mignon! Please be sure to check out the latest Grammar Girl episode to find out what math-related grammar questions I asked Mignon. And if you have any additional grammar-inspired math questions (or vice versa), please send them our way!

Also, remember to become a fan of the Math Dude on Facebook where you’ll find a new featured number or math puzzle posted every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at mathdude@quickanddirtytips.com.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Red wooden dice from Shutterstock