Probability is a perennial dreaded GMAT topic by students of all scoring levels. It’s hard enough to master concepts that you haven’t seen since high school, such as triangles and exponents, but probability is a topic that many test takers have never seen before, unless you did a little research before your last trip to the casino (in which case you may have decided to stay home instead!).
There are three tenets of probability theory that underlie every probability question on the GMAT, each of which follows from the last. You’ll still have to put some practice in on your own to really get the concepts down, but these are a good start:
1) The Definition of Probability
At its most basic, the probability of a desired event is equal to (Number of Desired Outcomes) / (Number of Total Possible Outcomes). So, if you want to know the chances of randomly picking a red grape from a bowl with 10 grapes, 3 of which are red, your probability is 3/10, or 30%.
2) The Range of Probabilities
Since the number of desired outcomes can’t be greater than the number of total possible outcomes—for example, you can’t have 11 red grapes in a bowl of only 10 grapes—all probabilities lie between 0 and 1. Also, the sum of all possible outcomes will always add up to 1. To extend the example from Rule 1, (Probability of picking a red grape) + (Probability of NOT picking a red grape) = 1, and so, manipulating algebraically, (Probability of picking a red grape) = 1 – (Probability of NOT picking a red grape). Realizing this tenet can help dramatically with time-consuming advanced probability questions on the GMAT.
3) Combining and Manipulating Probabilities
The toughest probability questions will have lots of events bouncing around and require you to deal with them in combination. In performing these, follow this rule of thumb, which is a consequence of all probabilities being numbers between 0 and 1: if the combination of two probabilities will result in a smaller number, like finding the probability of heads on two consecutive coin flips, then multiply the probabilities; if the combination should result in a larger number, then add them.
So, to answer the question of this post’s title, 1 – (Probability You Won’t Ace the GMAT) = (Probability You Will Ace the GMAT), which will definitely go up with the confidence and skill that comes with a little time spent studying probability.
