By: Apex GMAT

Contributor: Altea Sulollari

Date: 20th November 2020

GMAT probability questions, which test logical reasoning skills, tend to be quite daunting. The good news is that they don’t appear very frequently; the Quant section contains no more than three or four probability questions. However, since so many test-takers struggle with these questions, mastering probability can be an excellent way to boost your overall score.

GMAT probability questions aren’t so hard once you’ve grasped the basic concepts. Like the majority of the Quant section, probability questions only cover high school level material. The principle challenge is the tricky wording.

This article will cover some methods to simplify probability questions and boost your Quant score.

**What Is Probability?**

The first step to mastering probability is to break down the basic idea:

*Probability = the number of desired outcomes / the total number of outcomes*

Or in other words, the *chance of something happening is the quotient of the number of desired outcomes and the total number of possible outcomes*.

A coin flip is one generic example that can help us understand probability.

There are two possible outcomes when we flip a coin: *heads *or *tails*. If we want the coin to land on *heads*, then we divide 1 (the chance that the coin will land on the desired outcome, *heads*) by 2 (all possible outcomes, *heads *and *tails*), and the result is ½ or 0.5 (50%), meaning that there is a **50% chance** that the coin will land on *heads*.

Although this is an elementary example, it demonstrates the fundamental concept behind all probability problems–a ratio between a *part *and a *whole *expressed as a fraction or percentage.

**Probability of Independent Events**

The probability of *x *discrete events occurring is the product of all individual probabilities.

For example, imagine that we toss a coin twice. Each toss is independent of the other, meaning that each toss has an equal chance of landing on either *heads *or *tails *(0.5). If we want to calculate the chance of getting *heads *twice in a row, we need to multiply the probability of getting *heads *the first time by the probability of getting *heads *the second time.

Or, represented as an equation:

½ x ½ = ¼

We get a 0.25 or** 25% chance** that the coin will land on *heads* twice.

**Probability of Getting Either A or B**

Keep in mind that the sum of all possible events is equal to 1 (100%).

If we continue with the coin toss example, we know that the probability of landing on *heads *is 0.5, and that the probability of landing on *tails *is also 0.5. Therefore:

0.5 + 0.5 = 1

The possibility of landing on either *heads *or *tails *is equal to 1, or **100%**. In other words, every time we flip a coin, we can be certain that it will land on *heads *or *tails.*

**Probability Of An Event Not Occurring**

Following the concept that the sum of all possible events is 1, we can conclude that the probability of *event A* **not **happening (A’) is 1 – A, or equal to the probability of event B occurring.

The chance that the coin will not land on *heads *is equal to the chance that the coin will land on *tails*:

1 – 0.5 = 0.5

This method is most useful in situations with many favorable events and fewer unfavorable ones. Since time management is essential on the GMAT, it’s better to avoid solution paths that require more calculations. Subtracting the number of unfavorable events from the whole is quicker and simpler, and thus, less likely to result in mistakes.

**Pay Attention to Keywords**

Read each problem’s wording with great care to determine exactly which operations to use.

For example, if the problem uses the word “and,” you need to find the *product *of the probabilities. If the question uses the word “or,” you need to solve for their *sum*.

If we flipped one coin and we wanted to know the chances of landing on either *heads *or *tails*, we would calculate it like this:

0.5 + 0.5 = 1

Similarly, if we were to toss two coins and we wanted to find the probability of landing on both* heads *and *tails*, we would use this equation:

0.5 x 0.5 = 0.25

**Avoid Common Errors**

Minor errors, such as missing possible events, can lead to incorrect answers.

These pointers will help you avoid some common mistakes on probability questions:

- List all possible events
**before**starting any calculations; - Sum up the probabilities of all possible events to make sure they add up to 1;
- If there are several different arrangements possible (for example, picking different colored balls from a box), find the probability of one of the events and multiply it by the number of different possible arrangements.

If you enjoyed this article make sure to check out our other How To articles like: Efficient Learning & Verbal section.