Probability was initially developed for gambling. Given the gamblers I know, that means it can’t be particularly complicated.
Why we base the global financial system on it is another question, but Quantum Mechanics uses it as well, so I’ll admit I’m being judgmental here.
Looked at one way, Probability attempts to give us a mathematical way to predict the future, which isn’t necessarily the most accurate. It’s a bit like trying to predict the weather if you live somewhere other than London (for me, it’ll be rainy and grim).
CORRECT Probabilistic Thinking is Not Common
Or maybe lots of people think that they are good at it, or they “have a system,” or some other nonsense, but they are actually completely terrible at it.
THAT PERSON IS NOT YOU.
What it means that other people are terrible at Probability is that you get a bunch of language tossed around freely that means pretty much nothing.
In short, these people confuse likelihood with Certainty and overestimate the upside of something while downplaying the ever-present possibility that something catastrophic could happen (cf. 2008).
Now, in a very Zen sense, we cannot of course predict the future, so just maybe injecting a “maybe” actually is a very useful idea. To paraphrase Socrates by way of Don Rumsfeld, “there are unknown unknowns” in the world, so a bit of agnosticism wouldn’t harm any of us.
The problem comes, of course, in situations where we overreach and accidentally end up in that confused (and wrong) Certainty. Situations where this is useful are few and far between, and usually involve gambling; that is, the House likes to make money, and people who are too confident are easy marks.
So… any time we hear the words odds, chance, likelihood, or any mathematical “prediction” of the future, it’s time to put the skeptic’s hat on. There exists a good chance (hahahaha) that a deep misunderstanding is afoot.
Let’s start with a definition of “chance.” And it isn’t going to work to go tautologous and say something like “likelihood.” Let’s step inside the local William Hill (or on to that riverboat if you’re in the US) and make a guess.
Probability was Designed for Gambling
This isn’t a conjecture; it’s a real thing. Probability was originally developed to help bookmakers create odds so that the reliable bettors would be encouraged, more effectively, to part with their cheddar.
Then it might be little surprise that many GMAT Probability questions continue to involve finite game systems. That’s what the math is invented for!
Now it just might be that playing the horses or pretending to be Daniel Craig at the baccarat table with your clip-on bow-tie can, over time, instill a keen intuitive sense of Probability in a person. Try it and let me know how that goes. I’ll be waiting here.
If there’s any truth in that conjecture, I’d wager (hahahaha) that it’s because bettors have skin in the game. If they don’t get fairly good at these things, they’ll lose their shirts! It always helps to have a bit of incentive.
If you don’t understand Probability, the GMAT will ruin you.
That’s your skin in the game.
GMAT Probability might seem unapproachable, but that’s exactly why I’ve written this book: it is designed to be a fairly painless way to make sure that you DO UNDERSTAND the topic before you walk into the Test Center.
Let’s start with this: Some ways we misunderstand Probability
Many years ago, in the time when the band Creed dominated the airwaves, I worked as a radio DJ (don’t ask). Now, as it turned out, there was a tiny window that I faced while on the air.
Quite often, the weather report that I was legally obliged to read read “there is a 30% chance of rain.” And lo and behold, I would look out the window and it would be raining. But I would be legally obliged to say that there is a 30% chance of rain.
Clearly I used this as an opportunity to inform the wider public of basic Probability theory (and give them a good does of “Higher,” likely for the fourth time that hour, also legally obligated–cf. PAYOLA).
Those listeners loved me, I’m sure.
Second: Order of Selection Affects Probability, and this Confuses Folks
We simply don’t often think about the fact that selecting things in different orders affects the Probability outcome. Check this classic GMAT question:
If a family has four children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly two boys?
I mean it might seem that if you want four kids and want half of them to be boys, then the odds of that happening would be fifty-fifty.
Yet in practice, the probability is actually three-eighths. Just keep scratching your head for a moment: the answer, along with many others, is in the book…
Flipping a coin. Oh, the classic example again.
Let’s assume it’s a perfectly weighted coin that would never land on its side, etc. etc. In short, the chance for each flip is exactly 50-50 for Heads-Tails, respectively.
Let’s look at the following situation:
I’ve flipped this @%(*@$^! coin thirteen times and they have all been Tails! The next one MUST be Heads.
Well, actually, no. The Probability actually recycles every flip. What came before has NO MATHEMATICAL BEARING on what comes next. That means your Probability is now:
That’s it! If the previous outcomes don’t matter at all to the current outcome and therefore give us no sort of context for the next toss, the only thing that could possibly matter is the current toss.
The Past Predicts the Future, yet again.
Yet Another One: Fourth
If the universe really is infinite, then an infinite number of things that we would normally take for granted don’t have to happen.
If I drop a pen it might not fall.
The Sun might nova overnight and fail to rise tomorrow.
The Official Guide might give a useful explanation in the back.
I reiterate: these things COULD HAPPEN. Most anything, even in violation of the self-satisfied (and not always valid) laws of Newtonian Physics, could happen. Why do I say “most anything?”
Because there exists a chance that I’m wrong. (See what I did there?) However, the math will agree with me.
In short, something being possible doesn’t mean that it is going to happen or is even probability. It’s probably pretty damn unlikely. I wouldn’t hold my breath, but the math needs to account for it.
Other fallacies, such as Base Rate, Confusion of the Inverse, etc.
These are beyond the scope of what the GMAT will discuss and for this reason–as well as for your sanity–I will ignore them.
At the end of the day, however, Probability is too complex a topic to get into simply through one blog post or video:
Remember, Probability is one of the most misunderstood GMAT Quant topics.
It’s rarely taught in secondary school. It requires a different type of thinking from Arithmetic or Algebra. There are so many variations on it that it’s hard to know when to apply a specific formula.
Worst of all, it’s actually sort of nonsense because it’s trying to predict the future, which we know from Critical Reasoning is a no-no. Right?
Probability might be a bit of a dumb sort of math, but it’s on the GMAT to stay. The advantage of it is that, like other topics such as Standard Deviation, the GMAT only really scratches the surface.
If you get good at these basics, Probability questions will seem like free points.
How to get good? Glad you asked:
Rather than blind you with multiple variants of different probability equations, The GMAT Probability Guide presents the core concepts of Probability–
–and more… in ways that prove to you that Probability is actually totally accessible with a small shift in your thinking.
The GMAT Probability Guide shows you the basic ideas of Probability in plain language through numerous worked examples, and goes step-by-step through solutions ranging from the simplest to the most beastly GMAT Probability questions.
For those who are struggling to make their Probability skills meet what they know they’re capable of–these questions can’t be THAT difficult, can they?
No. They’re not. That’s the point.
The GMAT Probability Guide gives a slew of explanations, examples, and bad jokes that will take you all the way to Probability mastery.
I’m not saying that this book will solve all of your problems–but I wager it will solve the Probability-related ones. Yes, I said “wager.”
Read a few pages and see!