**By: ***Apex GMAT Contributor: Ilia Dobrev *

**Date:**August 12, 2021

The concept of probability questions is often pretty straightforward to understand, but when it comes to its application in the GMAT test it may trip even the strongest mathematicians.

Naturally, the place to find such types of problems is the Quantitative section of the exam, which is regarded as the best predictor of academic and career success by many of the most prestigious business schools out there – Stanford, Wharton, Harvard, Yale, INSEAD, Kellogg, and more. The simple concept of probability problems can be a rather challenging one because such questions appear more frequently as high-difficulty questions instead of low- or even medium-difficulty questions. This is why this article is designed to help test-takers who are pursuing a competitive GMAT score tackle the hazardous pitfalls that GMAT probability problems often create.

**GMAT Probability – Fundamental Rules & Formulas**

It is not a secret that the Quantitative section of the GMAT test requires you to know just the basic, high-school-level probability rules to carry out each operation of the practical solution path. The main prerequisite for success is mastering the Probability formula:

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

Probability P = | number of desired outcomes |

total number of possible outcomes |

We can take one fair coin to demonstrate a simple example. Imagine you would like to find the probability of getting a tail. Flipping the coin can get you **two** possible comes – a tail or a head. However, you desire a specific result – getting only a tail – which can happen only **one** time. Therefore, the probability of getting a tail is the number of desired outcomes divided by the number of total possible outcomes, which is **½**. Developing a good sense of the fundamental logic of how probability works is central to managing more events occurring in a more complex context.

Alternatively, as all probabilities add up to 1, the probability of an event not happening is 1 **minus **the probability of this event occurring. For example, 1 – ½ equals the chance of not flipping a tail.

**Dependent Events vs. Independent Events**

On the GMAT exam, you will often be asked to find the probability of several events that happen either simultaneously or at different points in time. A distinction you must take under consideration is exactly what type of event you are exploring.

** Dependent events** or, in other words,

**, are two or more events with a probability of simultaneous occurrence equalling zero. That is, it is absolutely impossible to have them both happen at the same time. The events of flipping either a tail or a head out of one single fair coin are disjoint.**

*disjoint events*If you are asked to find a common probability of two or more disjoint events, then you should consider the following formula:

Probability P of events A and B = | (Probability of A) + (Probability of B) |

Therefore, the probability of flipping one coin twice and getting two tails is **½ + ½**.

If events A and B are not disjointed, meaning that the desired result can be in a combination between A and B, then we have to subtract the intersect part between the events in order to not count it twice:

Probability P of events A and B = | P(A) + P(B) – Probability (A and B) |

** Independent events** or

**are two or more events that do not have any effect on each other. In other words, knowing about the outcome of one event gives absolutely no information about how the other event will turn out. For example, if you roll not one but two coins, then the outcome of each event is independent of the other one. The formula, in this case, is the following:**

*discrete events*Probability P of events A and B = | (Probability of A) x (Probability of B) |

**How to approach GMAT probability problems**

In the GMAT quantitative section, you will see probability incorporated into data sufficiency questions and even problems that do not have any numbers in their context. This can make it challenging for the test taker to determine what type of events he or she is presented with.

One trick you can use to approach such GMAT problems is to search for *“buzzwords”* that will signal out this valuable information.

**OR |**If the question uses the word “or” to distinguish between the probabilities of two events, then they are dependent – meaning that they cannot happen independently of one another. In this scenario, you will need to find the sum of the two (or more) probabilities.**AND |**If the question uses the word “and” to distinguish between the probabilities of two events, then they are independent – meaning their occurrences have no influence on one another. In this case, you need to multiply the probabilities of the individual events to find the answer.

Additionally, you can draw visual representations of the events to help you determine if you should include or exclude the intersect. This is especially useful in GMAT questions asking about greatest probability and minimum probability.

If you experience difficulties while prepping, keep in mind that *Apex’s GMAT instructors* have not only mastered all probability and quantitative concepts, but also have vast experience tutoring clients from all over the world to 700+ scores on the exam. Private GMAT tutoring and tailored customized *GMAT curriculum* are ideal for gaining more test confidence and understanding the underlying purpose of each question, which might be the bridge between your future GMAT score and your desired business school admissions.