GRE Probability Questions

Author

27-08-2024

Probability is one of the concepts in data analysis under the GRE quantitative reasoning. The other sections covered under the quant section are algebra, arithmetic, and geometry. The probability questions in the GRE assess your ability to evaluate uncertain events and make informed decisions using statistical principles. There aren't many probability questions on the GRE, except a maximum of three questions. If you aim for a high GRE score, even a single question matters, and it’s essential to master probability concepts. This article covers strategies and ideas that help to sharpen your problem-solving skills and achieve a high score.

What is Probability?

Probability is a measure of the likelihood that a particular event will occur. It ranges from 0 to 1, where 0 indicates an impossible event, and 1 indicates a certain event. The probability of an event A is often denoted as P(A). Probability questions assess your ability to determine the likelihood of various events. You might be asked to determine the probability of drawing specific items, selecting members from a group, or predicting outcomes based on given conditions.

Probability Formula

The probability of an event is determined by the formula

Probability= Number of favorable outcomes/ Total no of outcomes

For example: Consider flipping a fair coin. There are two possible outcomes: heads or tails. The probability of getting heads is:

P(heads)=Number of favorable outcomes/Total number of outcomes

P(heads) = ½

Similarly, the probability of getting tails is also

P(tails) = ½

Each outcome (heads or tails) has an equal chance of occurring, so the probability for each is 0.5 or 50%.

The two fundamental concepts that are tested on all GRE probability questions are Simple Probability, Permutation, and Combination.

Simple Probability

Simple probability is the likelihood of a single event happening during one trial or experiment. The set of all possible outcomes when we perform an experiment is called Sample space. For instance, when flipping a coin, the possible outcomes are "heads" and "tails." In this example, the sample space is:

S = {Heads, Tails}

Any subset of the sample space is called an event. So, let's say "getting heads" is an event, which corresponds to the outcome {Heads}. The probability of getting heads is the number of outcomes that constitute the event divided by the total number of possible outcomes. The outcomes in an event are called its 'favorable outcomes.'

It's calculated by dividing the number of ways the event can occur by the total number of possible outcomes, assuming all outcomes have an equal chance of occurring.

GRE Probability problem

A jar contains 5 red, 3 blue, and 2 green marbles. If you randomly pick one marble from the jar, what is the probability that it will be blue?

Solution:

Identify the Sample Space (S)

The total number of possible outcomes is the total number of marbles in the jar.

There are 5 red + 3 blue + 2 green = 10 marbles in total.

So, the sample space S = 10.

Identify the Event (E)

The event we are interested in is picking a blue marble.

The number of blue marbles (favorable outcomes) = 3.

Calculate the Probability (P)

The probability of picking a blue marble is given by the formula:

Probability= Number of favorable outcomes/ Total no of outcomes

So, the probability of picking a blue marble from the jar is 3/10 or 0.3.

Explanation:

Out of 10 marbles, 3 are blue. Since you’re picking one marble at random, the chance (or probability) that it will be blue is 3 out of 10. This tells us that there is a 30% chance of picking a blue marble from the jar. Here, even numbers and odd numbers are not counted.

Permutation & Combination

Permutation & Combination are also tested in the GRE Probability section. To simplify, Permutations involve sequences where the order matters, while combinations involve groups where the order doesn't matter.

Now to understand the concept better, let's look at the example:

Formula for permutation:

If you have n distinct objects and you want to arrange r of them, the number of permutations is given by:

P(n,r) = n!/(n-r)!

Where n! (n factorial) is the product of all positive integers up to n.

1. Problem:

You have 5 different books, and you want to arrange 3 of them on a shelf. How many different ways can you arrange these 3 books?

Solution:

Identify the values of n and r:

n=5 (the total number of books)

r=3 (the number of books to arrange)

Use the formula: P(n,r) = n!/(n-r)!

P(5,3) = 5!/(5-3)! = 5!/2!

Calculate the factorials: 5!= 5*4*3*2*1 = 120

2!= 2*1 = 2

P(5,3) = 120/2 = 60

Explanation:

In this problem, the order in which the books are arranged matters, so we use permutations. By using the formula, we calculated that there are 60 possible arrangements for 3 books out of 5.

Formula for Combination:

C(n,r) = n!/r!(n-r)!

2. Problem:

A committee of 4 members needs to be formed from a group of 10 people. How many different ways can this committee be selected?

Solution:

Identify the values of n and r:

n=10 (the total number of people)

r=4 (the number of people to select)

Use the formula: C(n,r) = n!/r!(n-r)!

C(10,4) = 10!/4!(10-4)! = 10!/(4!*6!)

Calculate the factorials:

10! = 10*9*8*7*6! = 5040*6! = 5040*720 = 3628800

6!= 6*5*4*3*2*1 = 720

4!= 4*3*2*1 = 24

C(10,4) = 3628800/24*720 = 3628800/17280 = 210

Explanation:

In this problem, the order in which the committee members are selected does not matter, so we use combinations. By using the formula, we calculated that there are 210 possible ways to form a 4-member committee from 10 people.

Probability Practice Problems with Answers

1. A bag contains 4 red, 3 green, and 2 blue balls. If you randomly draw one ball from the bag, what is the probability that it is green?

a) 1/9

b) 1/3

c) 1/2

d) 3/9

Answer: b) 1/3

Explanation: The total number of balls is 4 + 3 + 2 = 9. The probability of drawing a green ball is 3/9 = 1/3.

2. What is the probability of rolling a sum of 7 when two dice are rolled?

a) 1/6

b) 1/12

c) 1/9

d) 1/36

Answer: a) 1/6

Explanation: There are 6 favorable outcomes (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of a total of 36 possible outcomes. So, the probability is 6/36 = 1/6.

3. How many different ways can the letters in the word "CAT" be arranged?

a) 3

b) 6

c) 9

d) 12

Answer: b) 6

Explanation: There are 3 letters, so the number of arrangements is 3! = 3 × 2 × 1 = 6.

4. In how many ways can a committee of 3 people be selected from a group of 7 people?

a) 21

b) 35

c) 42

d) 49

Answer: b) 35

Explanation: The number of combinations is given by C(7,3) = 7!/3!(7-3)! = (7×6×5)/(3×2×1) = 35

5. A deck of cards is shuffled, and one card is drawn. What is the probability that it is a king, given that it is a face card?

a) 1/3

b) 1/4

c) 1/12

d) 3/52

Answer: a) 1/3

Explanation: There are 12 face cards (J, Q, K in 4 suits) and 4 kings. The probability is 4/12 = 1/3.

6. How many different 4-letter words can be formed from the letters of the word "BRIGHT" if no letter is repeated?

a) 720

b) 360

c) 120

d) 24

Answer: a) 720

Explanation: There are 6 letters, and we need to choose 4. The number of permutations is

P(6,4) = 6!/(6-4)! = (6×5×4×3)/1 = 720

7. In how many ways can 5 students be chosen from a group of 10 students?

a) 120

b) 252

c) 300

d) 210

Answer: d) 252

Explanation: The number of combinations is given by C(10,5) = 10!/(5!××5!) = 252

8. A box contains 5 red and 5 black balls. If two balls are drawn at random, what is the probability that both are black?

a) 1/2

b) 2/9

c) 1/4

d) 5/18

Answer: b) 2/9

Explanation: The total number of ways to choose 2 balls from 10 is C(10,2) = 45. The number of ways to choose 2 black balls from 5 is C(5,2)=10. Thus, the probability is 10/45 = 2/9.

9. How many different ways can 5 people be arranged in a line?

a) 5

b) 25

c) 120

d) 720

Answer: c) 120

Explanation: The number of permutations of 5 people is 5! = 5 × 4 × 3 × 2 × 1 = 120.

10. A school has 8 teachers. In how many ways can a team of 3 teachers be selected to organize a function?

a) 56

b) 24

c) 120

d) 336

Answer: a) 56

Explanation: The number of combinations is C(8,3) = 8!/(3!(8-3!) = 56

Tips to Crack GRE Probability Questions

To improve your overall test score in GRE probability, following the below tips can be very helpful.

Find the probability questions: GRE questions won't be explicitly mentioned as probability-related, so you'll need to determine if the given question falls under probability. Look for keywords in the question such as probability, event, outcome, or random selection.
Find the difference between Permutation and Combinations: Learn and master these concepts, as they frequently appear in probability questions. It's important to grasp the differences between them and practice solving problems involving the arrangement and selection of objects, such as forming a committee from a group of candidates with designated roles.
Make sure to memorize the formulas: Memorizing the important formulas for probability, permutation and combination can help you a lot to solve the question quicker.
Practice real-time: Apply these concepts to real-life situations to make the theory more engaging. For example, imagine calculating the probability of drawing a specific card from a deck while playing a card game with friends.
Break down the given problem: If you approach a complex problem, break it down into small parts, solve and combine them. For example: If you encounter a question with multiple dice rolls, calculate the probability of each roll’s outcome one by one.
Grasp the context: Examine the events you’re working with to determine if they are mutually exclusive, independent, or dependent. This analysis helps you choose the correct probability formula for the given problem.
Read the question carefully: There may be clues or hidden details in the question. Failing to notice them can impact your answer. For example: You are drawing two cards from a standard deck without replacement. What’s the probability of drawing a black card followed by a red card? The replacement means that once you draw a card from the deck, you do not put it back before drawing the next card.
Make it simple: Use diagrams, tables, or charts to understand the problem better. For example, when handling multiple probability events, drawing a Venn diagram or tree diagram can help you visualize various paths and outcomes.
Practice well: To achieve a high score in the GRE Quantitative sections, it's essential to prepare thoroughly before the exam. By practicing challenging GRE questions, you’ll learn to handle a range of scenarios and problem types, which will boost your confidence.

About Author Sruthi Krishnan

Sruthi Krishnan, an accomplished MBA graduate with an unwavering passion for writing is a recognized expert in Study Abroad Services. With years of experience in the overseas education industry, she specializes in preparing test materials for a wide range of exams, including IELTS, TOEFL, GRE, SAT, PTE, and more. Her expertise extends to providing comprehensive guidance on crafting Statements of Purpose (SOPs), Letters of Recommendation (LORs), and various aspects of study abroad, from exam preparation to admissions procedures. She's an expert in helping study-abroad aspirants through informative articles for study destinations like Canada, the US, the UK, Australia, and more. Her passion for writing has led to the creation of numerous articles that serve as valuable resources for students making critical decisions about their international education journeys.

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