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Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company’s GMAT preparation courses.
Las Vegas entices millions of visitors each year with the promise of riches, but even gambling winners typically note that “what happens in Vegas stays in Vegas”, including the money that they won, spent on lavish meals, rounds of drinks, and other indulgences. More commonly, a short hot streak turns quickly into a loss, and most Vegas visitors go home having lost or at least spent more money than they wish they had.
Not so for Steve Wynn, the famous developer of Las Vegas’ newest and most elegant hotel/casinos, including Bellagio, Wynn, and Encore. Taking full advantage of the cardinal rule of Las Vegas probability – over time, the house always wins – Wynn has taken Las Vegas for well over a billion dollars of personal wealth and turned himself into a luxury brand name in the process. How did this real estate and casino developer even out-trump Trump in net worth? Among other things, Wynn used probability to his advantage, and you can do the same on the GMAT as you attempt to climb onto the Forbes list yourself.
In order to succeed on GMAT probability questions, you don’t need to have Rain Man facility with numbers, but rather a businessman’s knack for efficiency. Say that a question asks:
On three consecutive flips of a coin, what is the probability of receiving at least one ‘heads’?
In this case, there are several sequences that would produce “at least one” heads:
Heads, Tails, Tails
Heads, Tails, Heads
Heads, Heads, Tails
Tails, Tails, Heads
Etc.
This method may well get you to the correct answer, but it’s time consuming and has the potential for error if you miss or double-count one of the sequences. It’s much more efficient to understand that the opposite of “at least one heads” is “no heads”, and that the two statements are complementary – one and only one of those things will happen, so their probabilities must add up to 100%.
There is only one way to get “no heads” on three straight coin flips:
Tails, Tails, Tails
The probability of this sequence is ½ for the first tails, then ½ for the second, then ½ for the third, so it can be represented as:
½ * ½ * ½ = 1/8
If there is a 1/8 chance of getting no heads, then there is a 1 – 1/8 chance of getting the other possibilities, each of which gets you at least one heads. Therefore, there is a 7/8 chance of getting at least one heads.
When viewing probability problems that ask you for the probability of getting “at least one” of a certain outcome, think shrewdly and recognize that it will likely be easier to take the probability of “none” and subtract from 100%. Thinking like a casino billionaire like Steve Wynn will help you here – remember that, when it comes to probability on the GMAT, it’s often smartest to figure out the smaller probability that your opponent will win, and take the remainder as the larger probability that you come out on top.
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