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 CommonOr 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). The GMAT Probability Guide 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 GamblingThis 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. The GMAT Probability Guide 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 FolksWe 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…
Third: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:
one-halfThat’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 GMAT Probability Guide The Past Predicts the Future, yet again.