GMAT Probability: Prob. per Distribution and Equal Likelihoods

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: Ultimate Guide to GMAT Permutations and Combinations

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? Figuring out the … Read More

Collapsing Probabilities in GMAT Probability: Part Deux

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

GMAT Probability: Number of Distributions x Probability per Distribution

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

“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

How to Understand GMAT Factorials

How to Understand 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 best described as … Read More