GMAT Combinatorics: The Ultimate Guide to GMAT Factorials — the Three-Question Method If we don’t get the concept of Factorials straight, the rest of this–Permutations and Combinations, quite a lot of advanced GMAT fatoring, etc.–is never going to work. How to Think About GMAT Factorials in a Broad Sense The idea of a Factorial is … Read More
A GMAT Probability Question Fully Solved: An Exception to the “At Least” Rule? It’s difficult to say that there’s really an exception–after all, you can do any Probability question multiple ways, forward, backward, or even sideways. The question is just which of these ways will be most effective in the given situation. What is the … Read More
GMAT Probability per Distribution and Equal Likelihoods A bag contains red and blue balls. Exactly half of the balls are red, and the other half are blue. If four balls are removed from the bag, then replaced, what is the Probability that exactly three blue balls will be among those selected? First, let’s figure out … Read More
GMAT Combinatorics: an Introduction At the risk of blowing all the secrets too early, let’s do this at the beginning. If you can answer three Core Questions, you’ll be able to answer any Combinatorics question that the GMAT decides to throw at you. Here they are: How Many Spaces? How Many Choices? Does Order Matter? … Read More
A GMAT Probability Problem with Too Many Moving Parts — How to Deal With a Complex Problem by Isolating its Constituent Parts This problem is so complicated that it’s unlikely to be seen as an actual GMAT Probability question–that is, something you would see in such a complex form on the exam itself–but bear with … Read More
Collapsing Probabilities: Part Deux — for Part Un, Click Here This one I’m only doing with the “Collapsing Probabilities” technique. You’re welcome to do it by making your choice first, then multiplying by the number of potential choices. It’s just that I won’t. You can e-mail me if you need your hand held. Here’s the … Read More
Collapsing Probabilities in GMAT Probability Unsurprisingly, there’s more than one way to look at this phenomenon. Let’s take a look at this straightforward case… Bag 1 contains forty marbles numbered consecutively from 11 to 50. Bag 2 contains fifty marbles numbered consecutively from 41 to 90. If one marble is selected from each bag, what … Read More
GMAT Probability and Number of Distributions x Probability per Distribution The Independent Probability Case for GMAT Probability Now, let’s go back to the example from the previous page, which we can rephrase as this:If a coin is flipped five times, what is the Probability that it will land on Heads only once?That gives us a … Read More
“At Least” Problems in GMAT Probability Hey, remember how all the Probabilities have to be fractions less than one? I mean, after all, it’s reasonably rare for there to be a greater than 100% chance that something will happen. The other thing to bear in mind is that a full Probability–anything that is forgone conclusion–is … Read More
The Basic GMAT Probability Equations First, we need to establish some sort of general definition for the term Probability itself. You’ll most often hear Probability defined as some variant of: desired outcomes / total outcomes First things first: Probability is always a fraction, which, of course, could also be a percent (because these two statements, … Read More