GMAT Gurus Speak Out: On Birthdays and Probabilities

We’re back with the next installment in an occasional series on the Veritas Prep Blog, called “GMAT Gurus Speak Out.” Veritas Prep has dozens of experienced GMAT instructors around the world (all of whom have scored in the 99th percentile on the GMAT), and it’s amazing how much collective experience they have in preparing students for the exam. This new series brings some of their best insights to you. Today we have another installment from Ashley Newman-Owens, a Veritas Prep GMAT instructor in Boston.

Because Veritas Prep turned ten this summer (kids — they grow up so fast), and because there’s a 100% chance that you’re reading this right now, we bring you a post today on probability and birthdays.

Unless you’re stranger to the test, you already know that the biggest challenge of many a GMAT problem is translating a question whose phrasing makes it seem nearly unanswerable into a series of simple, eminently answerable questions. And probability questions are no exception, my friend.

Let’s say you have a dog, and you have a hidden two-pound bag of chocolate chips. Unfortunately, while you are at the library, the dog discovers the bag of chocolate chips, and when you get home, it’s a significantly-less-than-two-pound bag of chocolate chips. On the phone, the vet asks you how much chocolate Digby actually consumed. But this would be a very messy question to answer directly. So what do you do? What would be easy? You weigh the chocolate Digby didn’t consume, and you subtract that figure from the two pounds there once were.

What’s the link to probability? This: probability questions on the GMAT often ask you for that quantity you can’t measure directly – how much chocolate the dog ingested. But the answer to the “opposite” question is often sitting there totally calculable, and once you find that opposite answer, you simply swap it for the more mysterious part of the whole. The State of the Chocolate is characterized by a dichotomy: every single morsel falls into exactly one of the two categories — (1) eaten by the dog, or (2) still in the bag. Likewise with complementary probability: an outcome either does or doesn’t occur, and if you know the probability that it doesn’t occur, 1 – that probability gives you the probability that it does.

Let’s consider a classic, seemingly convoluted probability problem, known to probability-heads as the Birthday Problem. While we concede that this isn’t reeeally a possible GMAT problem, because it requires a calculator at the final step, the thought process, question manipulation, and generation of an expression to solve are all absolutely GMATastic. So without further ado…

What’s the minimum number of people, the Birthday Problem asks, you’d need to get in a room for it to be more likely than not that two of those people had the very same birthday? (Pretend that February 29th doesn’t exist, and suppose that among the 365 standard days of the calendar year, each is exactly as likely as any other to be someone’s birthday.)

A) 366
B) 365
C) 183
D) 60
E) 23

What’s your first instinct on this problem? That this had better be a big room? Because, seriously, how often do you meet someone with the same birthday as you? (Chances are only one out of 365 people you meet shares your birthday.) But ooh, maybe you are not part of the birthday pair — maybe it’s two non-you people who get the honor. How does this change your calculation? It complicates it frighteningly!

So, remember our plan: chocolate, dogs. Let’s see if we can construct this question differently. Tune in next week, when the solution will be revealed!

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