GMAT Quantitative Probability Questions With Answers

GMAT probability questions check your understanding of the likelihood of events occurring, an essential concept tested in the quantitative section of the exam. The ability to calculate probabilities accurately in the GMAT can significantly boost your overall score. These questions range from simple to complex scenarios and may involve independent events, dependent events, permutations, and combinations. Developing a strong grasp of probability concepts, along with mastering problem-solving strategies, will give you an edge in approaching these types of questions. 

Let’s magnify the various GMAT probability questions and how to answer them!

Understanding the Concept of Probability 

Probability is a fundamental concept that quantifies the likelihood of an event occurring. In the context of the GMAT, understanding probability is crucial as it can appear in various forms and complexity. Here, we'll break down the basic concepts to understand and solve GMAT probability questions.

Basic Probability Concepts for GMAT

1. Definition of Probability:

Probability measures how likely an event is to occur, calculated as the ratio of favorable outcomes to the total number of possible outcomes.​

2. Sample Space and Events:

• Sample Space (S): The set of all possible outcomes in a probability experiment.
• Event (A): A subset of the sample space. It can consist of one or more outcomes.

3. Types of Probability:

• Theoretical Probability: Based on the reasoning behind probability (e.g., the probability of rolling a 3 on a fair six-sided die is ⅙).
• Experimental Probability: Based on the actual results of an experiment (e.g., if a die is rolled 100 times and 3 appears 15 times, the experimental probability is 15/100 = 0.15)

4. Complement Rule:

The probability of an event not occurring is equal to 1 minus the probability of the event occurring.

𝑃(Not A)=1−𝑃(𝐴)

5. Addition Rule:

For any two events A and B, the probability that A or B occurs is:
P(A∪B)=P(A)+P(B)−P(A∩B)

If A and B are mutually exclusive (cannot happen at the same time):
P(A∪B)=P(A)+P(B)

6. Multiplication Rule:

For any two independent events A and B, the probability that both A and B occur is: P(A∩B)=P(A)×P(B)

If the events are not independent, adjust the formula to account for their dependence.

GMAT Probability Questions and Answers 

Probability questions on the GMAT test your understanding of event likelihoods, including independent and dependent events, combinations, and permutations. Below are some probability questions with step-by-step solutions to help you master the topic:

1. Probability of a Single Event

Question: A die is rolled. What is the probability of rolling a 4?

Solution:

• A standard die has 6 faces numbered 1 to 6.
• Total possible outcomes = 6.
• Favourable outcomes (rolling a 4) = 1.

Probability=Favourable outcomesTotal outcomes=16

Answer: 16

2. Probability of an Even Number on a Die

Question: What is the probability of rolling an even number?

Solution:

• Even numbers on a die: 2, 4, 6 (3 outcomes).
• Total possible outcomes = 6.

Probability=36=12

Answer: 12

3. Probability of Drawing a Red Card from a Deck

Question: What is the probability of drawing a red card from a standard deck of 52 cards?

Solution:

• A standard deck has 52 cards: 26 red (hearts and diamonds) and 26 black (clubs and spades).
• Favourable outcomes (red cards) = 26.
• Total outcomes = 52.

Probability=2652=12

Answer: 12

4. Probability of Drawing a Face Card

Question: What is the probability of drawing a face card (J, Q, K) from a deck?

Solution:

• Total face cards: 3 (J, Q, K) in each suit.
• Total number of suits = 4.
• Favourable outcomes = 34=12.
• Total outcomes = 52.

Probability=1252=313

Answer: 313

5. Probability of Rolling Two Dice and Getting a Sum of 7

Question: If two dice are rolled, what is the probability that their sum is 7?

Solution:

• Possible sums for rolling two dice range from 2 to 12.
• Favourable outcomes for a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
• Total favourable outcomes = 6.
• Total possible outcomes when rolling two dice = 66=36.

Probability=636=16

Answer: 16

6. Probability of Drawing Two Aces Without Replacement

Question: If two cards are drawn consecutively without replacement, what is the probability that both are aces?

Solution:

• Favourable outcomes for the first draw: 4 aces out of 52 cards.

PFirst ace=452

• After drawing 1 ace, 3 aces remain out of 51 cards.

PSecond ace=351

• Combined probability:

PBoth aces=452351=122652=1221

Answer: 1221

7. Probability of Getting Exactly 2 Heads in 3 Coin Tosses

Question: A coin is tossed 3 times. What is the probability of getting exactly 2 heads?

Solution:

• Total outcomes for 3 tosses = 23=8.
• Favourable outcomes: HHT, HTH, THH = 3 outcomes.

Probability=38

Answer: 38

8. Probability of Selecting 2 Red Balls from a Bag

Question: A bag contains 3 red balls and 2 blue balls. What is the probability of selecting 2 red balls if 2 balls are drawn at random?

Solution:

• Total ways to choose 2 balls from 5 = 52=10.
• Favourable outcomes (2 red balls): 32=3.

Probability=310

Answer: 310

9. Probability of an Event Not Happening

Question: A die is rolled. What is the probability of not rolling a 5?

Solution:

• Probability of rolling a 5 = 16.
• Probability of not rolling a 5 = 1−16=56.

Answer: 56

10. Probability of Rolling at Least One 6 in Two Dice Rolls

Question: If two dice are rolled, what is the probability of rolling at least one 6?

Solution:

• Probability of not rolling a 6 on one die = 56.
• Probability of not rolling a 6 on either die = 5656=2536.
• Probability of rolling at least one 6 = 1−2536=1136.

Answer: 1136

11. Probability of a Sum Greater Than 9 with Two Dice Rolls

Question: What is the probability of rolling a sum greater than 9 with two dice?

Solution:

• Favourable outcomes for sums greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6).
• Total favourable outcomes = 6.
• Total outcomes for two dice = 36.

Probability=636=16

Answer: 16

12. Probability of Rolling Doubles on Two Dice

Question: What is the probability of rolling doubles (same number on both dice)?

Solution:

• Favourable outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6).
• Total favourable outcomes = 6.
• Total outcomes for two dice = 36.

Probability=636=16

Answer: 16

13. Probability of Selecting a Prime Number from 1 to 10

Question: If a number is selected at random from 1 to 10, what is the probability that it is a prime number?

Solution:

• Prime numbers between 1 and 10: 2, 3, 5, 7 (4 outcomes).
• Total outcomes = 10.

Probability=410=25

Answer: 25

14. Probability of a Correct Guess in a Multiple-Choice Question

Question: A multiple-choice question has 5 options. What is the probability of guessing the correct answer?

Solution:

• Total outcomes = 5.
• Favourable outcomes = 1.

Probability=15

Answer: 15

15. Probability of Selecting 3 People from a Group of 5

Question: What is the probability of selecting any 3 people from a group of 5?

Solution:

• Total ways to select 3 people from 5 = 53=10.
• Total possible combinations = 10.

Probability=1010 = 1

Answer: 1

Strategies to Ace the GMAT Probability Questions

Mastering GMAT probability questions requires a mix of understanding the core concepts and applying effective strategies. Below are detailed approaches to ensure success with these types of questions:

• Understand the Basics:
  Before attempting complex problems, it’s essential to solidify your understanding of basic probability concepts. The foundational formula for probability is:
  PEvent=Favourable OutcomesTotal Outcomes.
  It is also important to be familiar with key terms like independent events, dependent events, and mutually exclusive events. A solid understanding of these will provide a strong foundation for solving GMAT probability questions.

• Know the Types of Probability Problems:
  GMAT probability questions can typically be categorised into different types. Simple probability problems involve calculating the likelihood of a single event occurring. More complex questions may ask about combined events, where you need to compute the probability of multiple events happening together (AND/OR scenarios).
  There are also complementary probability questions, where you calculate the probability of an event not happening. Additionally, conditional probability, where the probability of one event depends on the occurrence of another event, is frequently tested. Recognising the type of probability problem will help guide you to the correct approach.

• Break Down Complex Problems:
  When facing complex probability problems, break them down into smaller, more manageable steps. The first step is to determine the total number of possible outcomes in the situation. Next, identify the number of favourable outcomes that satisfy the event you're trying to calculate.
  Finally, use the basic probability formula to calculate the likelihood of the event. For example, when asked to calculate the probability of rolling a certain sum with two dice, it’s helpful to list all the possible outcomes to ensure you don’t miss any favourable results.

• Practice with Permutations and Combinations:
  A significant number of GMAT probability problems involve selecting or arranging objects, making permutations and combinations essential skills. Permutations are used when the order of events matters, and the formula is given by:
  Pn,r=n!n−r!.
  Combinations are used when order does not matter, and the formula is:
  Cn,r=n!r!n−r!.
  Understanding and practising these formulas will help you tackle questions involving multiple events and outcomes more easily.

• Leverage Complementary Probability:
  In many cases, calculating the probability of an event not occurring is simpler than calculating the event itself. By using complementary probability, you can find the probability of an event by subtracting the probability of the event not happening from 1.
  For example, if a problem asks for the probability of getting at least one 6 when rolling two dice, you can calculate it as:
  PAt least one 6=1−PNo 6 on both rolls.
  This approach often simplifies problems and helps save time.

• Draw Diagrams or Use Tables:
  Visual aids, such as tree diagrams or tables, are extremely helpful for breaking down more complex probability questions, especially those that involve multiple events or conditional probability.
  Drawing out the problem can help you keep track of different possibilities and outcomes. This is especially useful in multi-step probability problems where there are different conditions to consider.

• Practice Time Management: GMAT probability questions can sometimes be tricky and time-consuming. If you come across a problem that seems overly complicated, it’s a good strategy to mark it for review and move on to easier questions first.
  You can return to the more difficult problem later with a fresh perspective. Practising time management during your preparation is key to ensuring you can complete all the questions within the given time frame.

From the Desk of Yocket

Probability is one of the most important topics in the GMAT Quantitative section, but it is also one of the more straightforward ones if you approach it with the right strategy. To deal with GMAT probability questions successfully, it's important to understand the underlying concepts and practice solving various types of problems. 

The more problems you practice, the more you’ll learn to identify patterns and use the most effective methods for each scenario. Yocket Prep offers structured resources to guide you through each step of your GMAT preparation, ensuring you're fully equipped to succeed on test day. Keep practicing, and remember, consistent effort leads to great results.