gmat probability problem article
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 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.

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Posted on
06
Aug 2020

Probability GMAT Problem

Probability GMAT Problems can be super complex if you don’t frame it correctly. One of the keys to looking at probability problems, particularly conditional probability and independent probability problems, is breaking each part up into its own entity, and a lot of times this clarifies the problem.

Introduction To The XYZ Probability Problem

Let’s take a look at this ‘XYZ’ probability problem. Xavier, Yvonne, and Zelda are solving problems. We’re given the 3 probabilities for correct answers and we’re being asked what’s the probability of X being right and solving it, Y solving it, and Z not solving it.

The first thing we can look at is, say: “Well what’s the probability of Zelda not solving it?” And it’s just going to be the flip, the other side of 5/8 to bring us up to 1. If she solves it 5 out of 8 times, she’s not going to solve it the other 3 out of 8 times. So, we’re dealing with 1/4, 1/2, and 3/8.

Doing The Math May Seem Simple

The math here is straightforward, multiply them together. But that might not be readily apparent, or at the very least, just plugging it into that formula can get you into trouble. So, here’s where owning it conceptually and mapping it out with a visualization helps you take command of this problem. 

Xavier Getting It Correct

Since each probability is independent of the others we can look at them independently. What’s the probability of Xavier getting this correct? 1 out of 4 times. So, we can say in general, for every four attempts, he gets it correct once or 25%. If, and only if Xavier gets it correct can we move on to the next part – Yvonne.

Yvonne Getting It Correct

Xavier gets a correct 1 out 4 times then what are the chances that Yvonne gets a correct? 1 out of 2. So to have Xavier get it correct and then Yvonne get it correct it’s going to be 1 out of 8 times – 1/4 times 1/2.

It’s not that we can’t look at a Yvonne when Xavier gets it incorrect, it’s that it doesn’t matter. From a framing perspective, this is all about only looking at the probability for the outcome that we want and ignoring the rest.

Zelda Getting It Incorrect

Xavier: 1 out of 4, Yvonne: 1 out of 2, gets us to 1 out of 8. Then and only then, what are the chances that Zelda gets it incorrect? 1 out of 8 trials brings us to X and Y are correct, then we multiply it by the 3/8 that Zelda gets it incorrect. That gets us to 3/64. 3 out of every 64 attempts will end in ‘correct’, ‘correct’, ‘incorrect’.

This is one of those problems that may have to go through a few times but once you attach the explanation to it, you can’t mess up the math.

If you enjoyed this GMAT probability problem, try your hand at these other types of challenging problems: Combinatorics & Algebra

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