CAT Success : Expert Tips on Probability, Intro to Data Sufficiency, Synonyms & PYQs Discussion- Day 39

Part-1: Quantitative Aptitude for CAT 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

1. 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.

2. Random Experiment probability problems

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

3. Sample Space: Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.

4. Event: Any subset of a Sample Space is an event.

5. 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.

6. 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.

7. Independent Events: The occurrence or non-occurrence of one event does not influence the occurrence or non-occurrence of the other.

8. 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.

Previous Year CAT Questions On Probability, Permutations And Combinations

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]

1. 0.91

2. 0.5

3. 0.49

4. 0.36

5. 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. 1/6

2. ¼

3. 1/5

4. 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

1. 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

2. P(S) = 1

3. 0 ≤ P (E) ≤ 1

4. P(ϕ) = 0 (∵ Probability of occurrence of an impossible event = 0)

5. 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

6. Learn Conditional Probability.

7. Binomial Distribution:”

P (r successes in n trials) =

8. 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 =

9. Practice sample papers and questions based on previous years CAT Questions.

10. Solve Questions from easy to moderate levels and after that try hard questions.

CAT entrance exam: Prerequisite to probability questions

Know this before probability permutations and combinations

1. Factorial

2. Permutation and Combination

3. Basics of Set Theory

CAT study material: References to Study (Theory)

For probability problems and concepts

1. NCERT Class 11 Maths

2. Mission CAT (YouTube, Link: https://www.youtube.com/watch?v=99zr_7OogIM)

CAT study material: References to Practice probability questions

1. How to prepare quantitative Aptitude for CAT by Arun Sharma.

2. CAT Funda (CAT PYQs; YouTube:://www.youtube.com/watch?v=nTqInfzG5yw)

3. CAT probability questions with solutions pdf.

Part-2: CAT 2025 Preparation Tips for Logical Reasoning and Data Interpretation

CAT 2025 Syllabus Topic: Strategy to prepare “Data Sufficiency in LR (Part-1)” for CAT

CAT Exam: About Topic/ Formulas

1. While the genre of Data Sufficiency is unique, the structure is not – all Data Sufficiency questions are structured the same, with three key elements:

2. The question stem: may or may not contain important facts

3. The statements: always two statements

4. 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]

1. Statement I alone is sufficient to answer this question but statement II is not sufficient to answer this question.

2. Statement II alone is sufficient to answer this question but statement I is not sufficient to answer this question.

3. None is sufficient to answer this question.

4. 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

1. 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?

2. A statement is sufficient when it guarantees exactly one (and only one) answer to the question.

3. You do not have sufficient information if more than one answer is possible

4. Do not solve the question after the moment you know the unique answer can be found thereafter.

5. 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.

6. Stick to the basics.

CAT entrance exam: Prerequisite

1. Blood Relation

2. Direction Sense, Ranking, Coding-Decoding, Inequality, Cubes, and various other basic topics of Logical Reasoning.
   
   

References to CAT Study (Theory)

1. LRDI by Nikhil K. Sinha

2. (YouTube link: https://www.youtube.com/watch?v=Fw6oK3aWuXw)

CAT References to Study (Practice)

1. Verbal and Non-Verbal Reasoning by R S Agrawal.

2. MBA Entrance Previous years Papers and Sample Papers.

3. https://www.youtube.com/watch?v=blkzss4S0-0

Part-3: CAT Exam Preparation 2025 for Verbal Ability & Reading Comprehension Synonyms

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.

1. Acceleration

2. Surplus

3. Baiting

4. 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.

1. Asphyxiation

2. Containment

3. Prohibiting entry

4. 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.

CAT Exam Important Topic: CAT preparation strategy on “ English Synonyms for CAT (Part-1)”.

• 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

1. Vocabulary

2. Parts of Speech

References to Study (Theory)

1. Wren and Martin

2. Made Word Power Easy

3. CATking.in (https://www.youtube.com/watch?v=qXw3syyd_Ak)

CAT preparation: References to Study (Practice)

1. Big Book of Synonyms and Antonyms – English (Maple Press)

2. CAT Previous years Papers and other MBA Entrance Exams.

3. 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!