Key Probability Formulas and Their Applications in CAT Exam 2025

Quantitative Aptitude section mostly covers probability questions. You only need to focus on a handful of key formulas and their applications. In this article, you will explore the most important probability formulas for CAT 2025 preparation and practical ways to use them.

What is Probability?

Probability is a method to measure the chance of an event happening among all other possible outcomes. For example, if you toss a fair coin, the probability of getting heads or tails is 1 out of 2 or 0.5. One can represent this as:

P(Event)=Number of favorable outcomes/Total number of possible outcomes

This is the most basic formula, and knowledge of this basic idea will help you solve more complex problems in CAT.

Important Probability Formulas for CAT Exam

Students preparing for CAT exams must go through the basic formulas for CAT exams that are given below:

1. Basic Probability Formula

P (A) = n (A)/ n (S)

Where n(A) is the number of favourable outcomes for event A, and n(S) is the total outcomes in the sample space.

2. Probability of Complementary Event

Sometimes one may try to find the probability that an event does not happen. If A′ is the event that A does not happen, then:

P (A′) = 1− P (A)

For example, if you want to find the probability that you don’t get a number 6 on a dice roll, as 1−1/6 = 5/6.

3. Addition Rule (Union of Two Events)

If, as a student, you would want to know the probability that either event A or event B (or both) happens, you use:

P (A∪B) = P (A) + P (B) − P (A∩B)

Important Note: If the events are mutually exclusive and cannot happen simultaneously, then the last term becomes zero.

4. Multiplication Rule (Intersection of Independent Events)

If two events A and B are independent (one does not affect the other), then the probability of both happening is:

P (A∩B) = P (A) × P (B)

For example, the chance of getting heads twice in two-coin tosses is ½ × ½ = ¼

5. Conditional Probability

Sometimes you want the probability of event A given that event B has already occurred. This is:

P (A/B) = P (A∩B) / P(B),       P(B)≠0

This formula is extremely useful when you want to refine probability based on new information.

6. Bayes’ Theorem (for Advanced CAT Questions)

Bayes’ theorem helps in understanding reverse conditional probabilities:

P (A/B) = P(B/A) × P(A)/ P(B)

One may see questions where there is a need to update probabilities based on new evidence, and this formula becomes vital in such cases.

How Can You Apply Probability Formulas in CAT 2025?

You can refer to simple examples given below to understand the usage of formulas.

Example 1: Basic Probability

A bag contains 4 red pens and 6 green pens. The probability of picking a red pen is?

P (Red) = 4 / 4+6 = 4/10 = 0.4

It may seem surprising, but this kind of question is very common.

Example 2: Complementary Event

The probability that it rains tomorrow is 0.3. What is the probability that it won’t rain?

P (No rain) = 1 − 0.3 = 0.7

Example 3: Addition Rule

In an exam, the probability of passing in Math is 0.6, and Hindi is 0.7. Passing both is 0.5. What is the probability of passing at least one?

P (Math ∪ Hindi) = 0.6 + 0.7 −0.5 = 0.8

So, one can have an 80% chance of passing at least one subject.

Example 4: Multiplication Rule

If the probability of a student who clears Quant is 0.6 and Verbal is 0.7 independently, then the probability of clearing both Quant and Verbal is:

0.6 × 0.7 = 0.42

Final Tips for Key Probability Formulas and Their Applications

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Apart from the formulas and examples explained above, note down the following tips as well for scoring higher

• Practice the above formulas regularly with previous year questions and sample CAT questions that help in building speed and accuracy.
• Understand the nature of the events: Are they independent? Mutually exclusive? This impacts which formula you use.
• Draw Venn diagrams and sample space charts to visualize problems, as it makes complex problems simpler.

Probability isn’t as hard as it looks if the concepts are clear. You can easily solve the CAT 2025 Quantitative section if you remember the basic formulas. Solving becomes easier if you have confidence and you have mastered the concepts by practicing their applications. Keep practicing real-life problems, and these formulas will become easier for you. One must solve as many mock tests as possible for better understanding and clarity.

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