IPMAT Probability Questions 2027: Topic-wise Solved Set + Free PDF Download

Probability is a topic in IPMAT Quantitative Aptitude which at first may seem intimidating but becomes a lot simpler when the fundamental concepts are understood.

The IPMAT Probability questions generally check if you can identify the total number of possible outcomes, determine the number of favourable outcomes and apply the correct probability formula without getting bogged down by unnecessary calculations.

It is important for students who are preparing for the IPMAT Indore and IPMAT Rohtak to practice IPMAT Probability Questions since Probability is part of the Quantitative Aptitude syllabus.

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The present syllabus for Quantitative Aptitude in IPMAT includes Probability as well as other topics such as Permutations & Combinations, Algebra, the Number System, Geometry and Arithmetic.

The article combines important Probability Questions for IPMAT together with their answers and detailed solutions. It also outlines the basic probability concepts which you should revise before tackling exam-level problems.

If you're after PDF materials on IPMAT Probability Questions, you can use this guide as a practice set and go along with IPMAT PYQs if you want more exam-focused practice.

Probability Questions for IPMAT in 2027: Overview

Probability is the mathematical way of measuring how likely an event is to happen.

The basic formula is: Probability of an event = Favourable outcomes / Total possible outcomes

For example, if a fair coin is tossed once, there are two possible outcomes:

• Head
• Tail

The probability of getting a Head is: P(Head) = 1/2

Probability always lies between 0 and 1.

• Probability = 0 means the event is impossible.
• Probability = 1 means the event is certain.
• A probability between 0 and 1 represents the likelihood of the event occurring.

These basic ideas form the foundation for most IPMAT Probability Questions.

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Important Formulas to Solve Probability Questions for IPMAT 2027

Before attempting IPMAT Probability Questions and Answers, revise these important formulas.

A clear understanding of these basic probability rules can help you solve Probability Questions for IPMAT 2027 more quickly and accurately.

Probability Concept	Formula	When to Use It
Basic Probability	P(E) = Favourable Outcomes / Total Outcomes	Use when all possible outcomes are equally likely.
Impossible Event	P(E) = 0	Use when an event cannot occur.
Certain Event	P(E) = 1	Use when an event is guaranteed to occur.
Complementary Probability	P(E') = 1 − P(E)	Useful when finding the probability that an event does not occur.
Addition Rule	P(A ∪ B) = P(A) + P(B) − P(A ∩ B)	Use when finding the probability of A or B occurring.
Mutually Exclusive Events	P(A ∪ B) = P(A) + P(B)	Use when A and B cannot occur together.
Multiplication Rule	P(A ∩ B) = P(A) × P(B)	Use for independent events occurring together.
Probability Range	0 ≤ P(E) ≤ 1	Every probability value must lie between 0 and 1.

IPMAT Probability Questions and Answers 2027

Here are practice questions based on the concepts IPMAT 2027 aspirants should know.

Question 1: Probability of Getting an Even Number

A fair die is thrown once. What is the probability of getting an even number?

Solution

A die has six possible outcomes: 1, 2, 3, 4, 5, 6

Even numbers are: 2, 4, 6

Therefore, favourable outcomes = 3.

Total outcomes = 6.

So,

P(Even number) = 3/6 = 1/2

Answer: 1/2

This is one of the simplest Probability Questions for IPMAT and is useful for understanding the basic favourable-outcome approach.

Question 2: Probability of Getting a Prime Number

A die is rolled once. What is the probability of getting a prime number?

Solution

The possible outcomes are: 1, 2, 3, 4, 5, 6

Prime numbers among these are: 2, 3 and 5.

Therefore:

Favourable outcomes = 3

Total outcomes = 6

P(Prime) = 3/6 = 1/2

Answer: 1/2

Question 3: Coin Toss Probability

A coin is tossed three times. What is the probability of getting exactly two Heads?

Solution

For three coin tosses, the total number of possible outcomes is:

2³ = 8

The outcomes containing exactly two Heads are:

• HHT
• HTH
• THH

Therefore, favourable outcomes = 3.

So:

P(Exactly two Heads) = 3/8

Answer: 3/8

This question introduces the connection between Probability and counting, which is useful for solving higher-level IPMAT Probability Questions.

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Question 4: At Least One Head

A fair coin is tossed three times. What is the probability of getting at least one Head?

Solution

Instead of calculating all outcomes containing one, two or three Heads separately, use the complement method.

The opposite of "at least one Head" is: no Heads

That means all three tosses must result in Tails.

Probability of three Tails: (1/2) × (1/2) × (1/2) = 1/8

Therefore: P(at least one Head) = 1 − 1/8 = 7/8

Answer: 7/8

IPMAT Probability Questions Based on Cards

Card-based problems are another useful category for Probability preparation.

A standard deck contains:

• 52 cards
• 4 suits
• 13 cards in each suit
• 26 red cards
• 26 black cards
• 12 face cards: Jack, Queen and King

Understanding these numbers makes card-based IPMAT Probability Questions and Answers much easier.

Question 5: Probability of Drawing a Red Card

One card is drawn randomly from a standard deck of 52 cards. What is the probability that it is red?

Solution

There are 26 red cards.

Total cards = 52.

Therefore: P(Red card) = 26/52 = 1/2

Answer: 1/2

Question 6: Probability of Drawing a King

One card is selected randomly from a standard deck. What is the probability that the card is a King?

Solution

There are four Kings in a standard deck.

Total cards = 52.

Therefore: P(King) = 4/52 = 1/13

Answer: 1/13

Question 7: Probability of Drawing a Face Card

A card is drawn randomly from a standard deck. What is the probability of getting a face card?

Solution

The face cards are:

• Jack
• Queen
• King

There are three face cards in each of the four suits.

Therefore: 3 × 4 = 12 face cards

Total cards = 52.

Hence: P(Face card) = 12/52 = 3/13

Answer: 3/13

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IPMAT Probability Questions Based on Balls and Boxes

Questions involving coloured balls are common practice problems because they test the candidate's ability to identify favourable and total outcomes.

Question 8: A box contains 5 red balls and 3 blue balls. One ball is selected randomly. What is the probability of selecting a blue ball?

Solution

Total balls: 5 + 3 = 8

Blue balls = 3.

Therefore: P(Blue) = 3/8

Answer: 3/8

Question 9: A bag contains 4 red, 5 blue and 3 green balls. One ball is drawn randomly. What is the probability that the ball is neither red nor green?

Solution

"Neither red nor green" means the ball must be blue.

Total balls: 4 + 5 + 3 = 12

Blue balls = 5.

Therefore: P(Blue) = 5/12

Answer: 5/12

The key here is translating the wording into the required event before applying the formula.

IPMAT Probability Questions Using Complementary Probability

Complementary probability is one of the most useful shortcuts for entrance-exam questions.

Question 10 A fair die is thrown twice. What is the probability of getting at least one 6?

Solution

There are 36 possible outcomes. Instead of counting every outcome containing a 6, calculate the probability of getting no 6.

Probability of not getting a 6 in one throw: 5/6

For two throws: 5/6 × 5/6 = 25/36

Therefore:

P(at least one 6) = 1 − 25/36 = 11/36

Answer: 11/36

IPMAT Probability Questions Using Permutations and Combinations

Probability and permutations and combinations are closely connected.

The current IPMAT Quantitative Aptitude syllabus includes both topics, so students should be comfortable moving between counting and probability-based questions.

Question 11: A committee of 2 students is selected from 5 boys and 3 girls. What is the probability that both selected students are girls?

Solution

Total students: 5 + 3 = 8

Number of ways to select 2 students: ⁸C₂ = 28

Number of ways to select 2 girls from 3: ³C₂ = 3

Therefore: P(Both girls) = 3/28

Answer: 3/28

This type of question is an excellent example of how Combinations and Probability work together.

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Higher-Level Probability Questions for IPMAT 2027

Once you are comfortable with basic questions, move to problems where the wording itself becomes part of the challenge.

Question 12: Two dice are thrown simultaneously. What is the probability that the sum of the numbers obtained is 8?

Solution

When two dice are thrown:

Total outcomes = 6 × 6 = 36

The outcomes whose sum is 8 are:

• (2, 6)
• (3, 5)
• (4, 4)
• (5, 3)
• (6, 2)

There are 5 favourable outcomes.

Therefore: P(Sum = 8) = 5/36

Answer: 5/36

Question 13 Two dice are thrown. What is the probability that the sum is greater than 9?

Solution

Possible sums greater than 9 are: 10, 11 and 12

For sum 10:

• (4,6)
• (5,5)
• (6,4)

For sum 11:

• (5,6)
• (6,5)

For sum 12:

• (6,6)

Total favourable outcomes = 6.

Total outcomes = 36.

Therefore: P(Sum > 9) = 6/36 = 1/6

Answer: 1/6

IPMAT Probability Questions 2027: Mixed Practice Set

Try these questions yourself before looking at the answers.

Question 14: A die is thrown once. What is the probability of getting a number greater than 4?

A.1/6
B. 1/3
C. 1/2
D. 2/3

Answer: B. 1/3

Question 15: A coin is tossed twice. What is the probability of getting at least one Tail?

A.1/4
B. 1/2
C. 3/4
D. 1

Answer: C. 3/4

Question 16: A card is drawn from a standard deck. What is the probability of getting an Ace?

A.1/13
B. 1/26
C. 4/13
D. 1/4

Answer: A. 1/13

Question 17: A bag contains 6 red balls and 4 blue balls. One ball is selected randomly. What is the probability of selecting a red ball?

A.2/5
B. 3/5
C. 1/2
D. 4/5

Answer: B. 3/5

Question 18:Two dice are thrown. What is the probability of getting a sum of 7?

A.1/12
B. 1/6
C. 1/9
D. 1/3

Answer: B. 1/6

Question 19: A box contains 3 white balls and 7 black balls. One ball is selected. What is the probability that it is not white?

A.3/10
B. 7/10
C. 1/2
D. 1/3

Answer: B. 7/10

Question 20:Three coins are tossed simultaneously. What is the probability of getting exactly one Head?

A.1/8
B. 1/4
C. 3/8
D. 1/2

Answer: C. 3/8

Probability Questions for IPMAT 2027: Common Mistakes to Avoid

Students may lose marks even if they understand the formulas due to minor errors.

Mistake 1: Using the Wrong Total

Before you calculate the number of favourable outcomes, you must first establish the sample space.

Mistake 2: Forgetting the Complement

"At least one" questions can get too long if you work out every possible case one by one.

Mistake 3: Assuming Events Are Independent

Check whether the first event changes the conditions for the second.

Mistake 4: Ignoring "Without Replacement"

If an item is removed from a collection and not returned, the total number of objects changes.

Mistake 5: Confusing Favourable Outcomes With Total Outcomes

The numerator represents what you want. The denominator represents all possible outcomes under the given conditions.

How to Prepare for IPMAT Probability Questions in 2027?

A practical preparation plan can be divided into four stages.

Stage 1: Learn the Basics

Start with:

• Sample space
• Events
• Favourable outcomes
• Basic probability
• Complementary probability

Do not move ahead until these concepts are comfortable.

Stage 2: Practise Standard Models

Solve questions based on:

• Coins
• Dice
• Cards
• Balls
• Numbers
• Selection

These problems help you recognise common patterns.

Stage 3: Combine Probability With P&C

Once the basics are clear, practise questions involving:

• Selection
• Arrangement
• Combinations
• Counting
• Probability

This is where many exam-level questions become more interesting.

Stage 4: Solve Previous-Year Papers

Finally, test yourself using actual IPMAT papers.

Toprankers provides IPMAT previous-year papers with solutions and covers papers from multiple years, which can help you understand how the exam has evolved.

You can also use the IPMAT Maths Preparation guide to build a broader Quantitative Aptitude strategy.

Why Practise Probability Questions for IPMAT?

Probability is included in the Quantitative Aptitude syllabus for IPMAT. The current Toprankers syllabus guide lists Probability among the Modern Mathematics topics, alongside Permutations & Combinations.

However, knowing the formula alone is not enough.

An IPMAT question can combine Probability with:

• Permutations
• Combinations
• Number systems
• Sets
• Counting
• Cards
• Dice
• Coins
• Selection problems
• Conditional situations

This is why solving different types of Probability Questions for IPMAT is more useful than memorising formulas in isolation.

The best preparation approach is to understand the concept first, then solve basic questions, followed by mixed and application-based problems.

IPMAT Probability Questions PDF: How to Use a PDF Effectively

Students searching for an IPMAT Probability Questions PDF often download a large collection of questions and start solving them randomly.

That is not necessarily the most effective approach.

Instead, organise your PDF practice into three levels:

Level	Type of Questions	Goal
Level 1	Basic formula-based questions	Build concepts
Level 2	Application-based questions	Improve accuracy
Level 3	Mixed Probability + P&C questions	Develop exam-level problem-solving

After completing each set, maintain a small error log.

Record:

• Question type
• Your answer
• Correct answer
• Why you made the mistake
• Shortcut or concept to remember

This turns an IPMAT Probability Questions PDF from a simple question bank into a useful revision resource.

For additional practice, you can also refer to Toprankers' IPMAT Sample Papers, where you can practise questions in a more exam-like format.

Conclusion

The most effective way of mastering Probability questions in IPMAT is to cease viewing Probability as a chapter based on formulas.

Rather, study how to identify the sample space, calculate the number of favourable outcomes, recognise complementary events, and determine when to use permutations and combinations.

Begin with some simple problems involving coins and dice, then progress on to those with cards, selections and questions based on counting. When you have a solid grasp of the basic concepts, practice solving a variety of IPMAT probability questions and answers within a time limit.

Most importantly, use previous-year papers to understand the level of questions you may face. Toprankers' current IPMAT resources include previous-year papers, sample papers, the Quantitative Aptitude syllabus and Maths preparation guidance, making it easier to move from concept learning to exam-oriented practice.

Plan Your Next Steps

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