CAT Admit Card Date:05 Nov' 25 - 30 Nov' 25
Hello CAT 2025 aspirants! The CAT 2025 exam will be held soon. This 60-day preparation guide by Careers360 is here to keep your preparation on track. Day 39 focuses on mastering probability questions, an essential part of the Quant section. This guide also includes tricky aptitude problems, data sufficiency sets, and high-frequency synonyms for CAT Preparation 2025 in 60 days. These focused strategies will enhance your problem-solving speed and accuracy for cracking the CAT 2025 MBA entrance exam.
Aspirants can also refer to the Permutation and Combination and Probability problems with solutions pdf.
CAT Exam Important Topic: Strategy to Prepare Probability Questions For CAT Exam, Permutation and Combination
Important Concept/Formula Used in CAT Probability Practice Questions
CAT Probability or Chance:
Probability is a quantitative measure of the chance of occurrence of a particular event.
PE=n(E)/n(S), n(E) = no of favourable events; n(S) = Sample Space.
Random Experiment probability problems
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If all the possible outcomes of an experiment are known but the exact output cannot be predicted in advance.
Examples
(i) Tossing of a fair coin (Total Outcome 2)
(ii) Dice probability questions
Throwing an unbiased die (Total Outcome 6)
(iii) Cards game probability questions
Drawing a card from a pack of shuffled cards
A pack or deck of playing cards has 52 cards which are divided into four categories as given below
a. Spades (♠)
b. Clubs (♣)
c. Hearts (♥)
d. Diamonds (♦)
[13 Cards: 9 Number cards, 1 Ace, 1 Jack, 1 Queen and 1 King] in each type
Sample Space: Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.
Event: Any subset of a Sample Space is an event.
Equally Likely Events: Events are said to be equally likely if there is no preference for a particular event over the other.
Examples
(i) When a coin is tossed, Head (H) or Tail is equally likely to occur.
Mutually Exclusive Events: if the occurrence of one of the events excludes the occurrence of the other
Example
(i) Tossing of a coin: either Head or Tail.
(iii) Rolling of a die: Either odd or even.
Independent Events: The occurrence or non-occurrence of one event does not influence the occurrence or non-occurrence of the other.
Exhaustive Event is the total number of all possible outcomes of an experiment.
Examples
(i) When a coin is tossed, we get either Head or Tail. Hence there are 2 exhaustive events.
Prepare for the CAT exam with previous year questions on Probability, Permutations, and Combinations. These topics test logical reasoning and analytical thinking. Practising PYQs helps you understand question patterns, boost accuracy, and manage time effectively during the Quant section.
Q1. Difficult aptitude questions on probability
A coin of radius 3 cm is randomly dropped on a square floor full of square-shaped tiles of 10 cm each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.[XAT 2018]
0.91
0.5
0.49
0.36
0.16
Solution: (E)
The radius of the coin is 3 cm. Since the coin should not cross the edge, the centre of the coin should at least be 3 cm away from the edge of the tile.
If we left 3 cm from all the edges, then the centre can lie in a square of 4 x 4.
So, Probability = Area of square 4 x4/ Area of tile
= 16/100 =0.16.
Q2. A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is [IPMAT 2019]
1/6
¼
1/5
1/10
solution: [C]
We can get sum 15 if
Case 1: 6, 6, 3
Total outcome = 3!/2! = 3
Favourable outcome (getting 4 at first throw) = 0
Case 2: 6, 5, 4
Total outcomes = 3! = 6
Favourable outcome (getting 4 at first throw) = 2 (4, 5, 6 or 4, 6, 5)
Case 3: 5, 5, 5
Total outcome = 1
Favourable outcome (getting 4 at first throw) = 0
Probability = 2/10 = 1/5.
Tricks and Tips of CAT permutations and combinations, probability
Learn Algebra of Events
(i) A ∪ B is the event that either A or B or Both occur. (i.e., at least one of A or B occurs)
(ii) A ∩ B is the event that both A and B occur
(iii) is the event that A does not occur
(iv) is the event that none of A and B occurs
P(S) = 1
0 ≤ P (E) ≤ 1
P(ϕ) = 0 (∵ Probability of occurrence of an impossible event = 0)
Let x outcomes be favourable to E and y outcomes are not favourable to E, then
Odds in favour of E are x:y, i.e.,x/y and
Odds against E are y:x, i.e.y/x
PE=x/x+y
PE'=y/x+y
Learn Conditional Probability.
Binomial Distribution:”
P (r successes in n trials) =
If n fair coins are tossed,
The Total number of outcomes in the sample space = 2n
The probability of getting exactly the r-number of heads when n coins are tossed =
Practice sample papers and questions based on previous years CAT Questions.
Solve Questions from easy to moderate levels and after that try hard questions.
Know this before probability permutations and combinations
Factorial
Permutation and Combination
Basics of Set Theory
CAT study material: References to Study (Theory)
For probability problems and concepts
NCERT Class 11 Maths
Mission CAT (YouTube, Link: https://www.youtube.com/watch?v=99zr_7OogIM)
CAT study material: References to Practice probability questions
How to prepare quantitative Aptitude for CAT by Arun Sharma.
CAT Funda (CAT PYQs; YouTube:://www.youtube.com/watch?v=nTqInfzG5yw)
CAT probability questions with solutions pdf.
CAT 2025 Syllabus Topic: Strategy to prepare “Data Sufficiency in LR (Part-1)” for CAT
CAT Exam: About Topic/ Formulas
While the genre of Data Sufficiency is unique, the structure is not – all Data Sufficiency questions are structured the same, with three key elements:
The question stem: may or may not contain important facts
The statements: always two statements
The answer choices: always the same.
Sample Question based on PYQs on Data Questions for CAT/ MBA Entrance Exam:
Q1. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?
I. Sixty per cent of the top academic performers were not athletes.
II. All the top academic performers were not necessarily athletes. [CAT 2007]
Statement I alone is sufficient to answer this question but statement II is not sufficient to answer this question.
Statement II alone is sufficient to answer this question but statement I is not sufficient to answer this question.
None is sufficient to answer this question.
Both statements together are sufficient to answer this question.
Solution: [A]
Statement I: 40% of top academic performers are athletes = 10.
Statement II: does not provide any relevant information.
So the answer is (1).
Tips and Tricks for CAT 2025
Ask yourself the following questions (starting with the statement (1):
Is the information in the statement (1) alone enough to answer the question?
Is the information in a statement (2) alone enough to answer the question?
Can an answer be given if with the information from statements (1) and (2) both?
A statement is sufficient when it guarantees exactly one (and only one) answer to the question.
You do not have sufficient information if more than one answer is possible
Do not solve the question after the moment you know the unique answer can be found thereafter.
If the answer from one statement alone and by combining both statements can be found out then the answer will be from one statement alone.
Stick to the basics.
CAT entrance exam: Prerequisite
Direction Sense, Ranking, Coding-Decoding, Inequality, Cubes, and various other basic topics of Logical Reasoning.
References to CAT Study (Theory)
LRDI by Nikhil K. Sinha
(YouTube link: https://www.youtube.com/watch?v=Fw6oK3aWuXw)
CAT References to Study (Practice)
Verbal and Non-Verbal Reasoning by R S Agrawal.
MBA Entrance Previous years Papers and Sample Papers.
https://www.youtube.com/watch?v=blkzss4S0-0
Sample Questions:
Directions: Choose a similar word from the given options for highlighted phrase/word.
Q1. Public policy in regard to food in main economies around the world has not provided adequate incentive, and the response to emergencies like accidents is equally sad.
Acceleration
Surplus
Baiting
Encouragement
Ans: D
Explanation: The context of the sentence refers to Encouragement. Hence option D is correct.
Q2. We today can see a swing away from these stereotypes, or have they established a stranglehold on our perceptions.
Asphyxiation
Containment
Prohibiting entry
Overwhelming control
Ans: D
Explanation: Asphyxiation- it happens when someone is literally strangled. And here the context is different.
Containment: it cannot be established and hence can be eliminated.
It does not seem appropriate here.
Prohibiting entry is for physical context and not for abstract. Hence can be eliminated.
Overwhelming control is a perfect fit here. Hence option D is correct.
One needs to be careful about the context.
Every word in the English language has a lot of different meanings.
To learn synonyms one can create word families
Beautiful- Gorgeous, Dazzling, Splendid, Magnificent
Important- necessary, vital, critical, Indispensable
One can also take reference from root words.
One can learn synonyms by logically associating a word with a sentence or a situation.
One needs to carefully observe the sentence's meaning as a whole.
Another method is to eliminate the other options.
Practise more and more exercises.
Prerequisite to CAT Exam Preparation
Vocabulary
Parts of Speech
References to Study (Theory)
Wren and Martin
Made Word Power Easy
CATking.in (https://www.youtube.com/watch?v=qXw3syyd_Ak)
CAT preparation: References to Study (Practice)
Big Book of Synonyms and Antonyms – English (Maple Press)
CAT Previous years Papers and other MBA Entrance Exams.
CATKing.in (YouTube; Link: https://www.youtube.com/watch?v=qXw3syyd_Ak&t=6s )
We will be back with Day 40 tomorrow. Do practice and be focused.
Thank you! All the best!
Frequently Asked Questions (FAQs)
Not always. CAT probability questions are logic-based. With clarity on concepts, you can solve most in under 2 minutes.
Solve PYQs to understand exam trends, question framing, and difficulty levels. They’re the best resource for realistic preparation
Focus on basic probability rules, conditional probability, Bayes' theorem, and card/dice problems for better accuracy in CAT 2025.
Understand the question, evaluate each statement independently, then together. Avoid solving and focus on sufficiency only, not exact answers.
Synonym questions test contextual understanding. Practice with CAT-level RCs, vocabulary lists, and PYQs to build word-sense skills.
On average, in the quantitative aptitude section of the CAT exam, you might expect to see around 2 to 4 questions related to probability. This is a rough estimate based on historical data up until 2024.
On Question asked by student community
Hello,
With 802 marks in TS Inter and ST category, you have a fair chance of getting admission in BPT (Bachelor of Physiotherapy) in some private colleges through state counselling.
However, for government colleges, the cutoff may be slightly higher, so keep options open for management quota or allied health colleges too.
Hope you understand.
Hey,
You already have a strong profile with the score of 58% in Class 10, 74% in Class 12, and 80% in graduation, but admission in IIT Bombay, Shailesh J Mehta School of Management is quite competitive, especially if you are in general category because the cutoff for general goes to 98.5-99%. Your CAT percentage is impressive but your 10th marks might reduce your score during the shortlisting process. If you perform well in Written Ability Test and Personal Interview, and present your commerce background you still stand a fair chance. But it would also be wise if you have some backups like MDI Gurugram, IMT Ghaziabad, IMI Delhi, where your marks and profile will fit well in their selection range.
HELLO,
I am providing you the link below through which you will be able to download the previous 10 years CAT question papers
Here is the link :- CAT Previous year Question papers
Hope this Helps!
The three key formulas that can solve almost all Profit & Loss problems are:
Profit/Loss % = (Profit or Loss / Cost Price) × 100%, where CP is the cost price.
Discount % = (Discount / Marked Price) × 100%, where MP is the marked price.
Mark up % = (Mark up Value / Cost Price) × 100%, where CP is the cost price.
These formulas can be adapted for problems involving discounts, marked price, or successive gains/losses.
For detailed examples and variations, you can from the article
Hello,
Yes, Pragati Engineering College offers seats in Category-B (Management quota) for B.Tech programmes. The selection criteria is mentioned as the per the guidelines issued by the AP State Council of Higher Education (APSCHE). The applications are available on the college's official website.
You can know more about the college and the courses from the link given below:
https://www.careers360.com/colleges/pragati-engineering-college-surampalem
Hope it helps!!!
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
September 2020
May 2021
January 2021
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
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