GMAT Probability Problems
Posted on
12
Aug 2021

GMAT Probability Problems – How to Tackle Them & What Mistakes to Avoid

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 = 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, disjoint events, 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.

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 discrete events 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:

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.

Read more
Posted on
20
Nov 2020

GMAT How-to: Probability Problems

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 principal 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.

 

Contributor: Altea Sulollari
Date: 20th November 2020

Read more