45+ CAT Probability, Combinatorics Questions PDF With Video Solutions

Probability topic an important part of the CAT. You can expect close to 2-3 questions in the latest 22 question format of the CAT Quant section. Here, some of the important probability questions for the CAT Exam. If you want to practice these important probability questions, you can download the PDF, which is completely Free. Probability is often one of the most feared topics among the candidates. 

It is not a very difficult topic if you understand the basics of Probability well. Practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked in CAT Exam. Probability-based questions appear in the CAT test almost every year. A lot of aspirants avoid this topic but remember that one can definitely solve the easy questions on Probability if one is thorough with the basics. Therefore, practising questions with Probability should not be avoided. The chances of occurring or not occurring an event should be determined based on the number of favourable and not favourable conditions.

Here we are giving some very important probability questions, which also include questions from the CAT previous papers. The candidates are advised to try each question on their own and later go through the solutions given below. Note: No sign-up is required to download the questions PDF

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CAT Probability And Combinatorics Formulas PDF

CAT Probability and Combinatorics are among the important topics in the quantitative aptitude section, and it is vital to understand the formulas related to them clearly. Enrolling in a CAT online coaching will ease up your process and help you understand the concepts better.

To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve Progressions and series questions with ease and speed. Click on the below link to download the CAT Progressions and series formulas PDF. Check with CAT exam syllabus to know similar other important topics that are important for the CAT exam.

1. Basics of Probability

If the probability of an event occurring is p, then the probability that the event will occur r times in n trials is given by = $$ ^{n}\textrm{C}_{r}p^{r}(1-p)^{n-r} $$

If p is the probability of an event, then odds in favor of an event are p / (1 – p). Conversely, the odds against are (1-p)/p.

Say $$E_{1}, E_{2}…. E_{n} $$ are mutually exclusive exhaustive events with probabilities $$p_{1}, p_{2}.... p_{n}$$ and expected values $$e_{1}, e_{2}.... e_{n}$$ then Expected payoff = $$\sum_{i=1}$$ $$^{n}p_{i}e_{i} $$

2.  Bayes theorem:

Let $$E_{1}, E_{2}, E_{3}...$$ be mutually exclusive and collectively exhaustive events each with a probability $$p_{1}, p_{2}, p_{3}...$$ of occurring. Let B be another event of non-zero probability such that probability of B given $$E_{1}$$ is $$q_{1}$$, B given $$E_{2}$$ is $$q_{2}$$ etc. By Bayes theorem: $$$P(E_{i}/B) = \frac{p_{i}q_{i}}{\sum_{j=1}^{n}p_{j}q_{j}}$$$

3. Derangements

If n distinct items are arranged, the number of ways they can be arranged so that they do not occupy their intended spot is $$D = n!$$($$ \frac{1}{0!}$$ - $$\frac{1}{1!}$$ + $$\frac{1}{2!}$$ - $$\frac{1}{3!}$$ + .... + $$\frac{(-1)^{n}}{n!}$$)

For, example, Derangements of 4 will be D(4) = $$4!\left(1-\dfrac{1}{1!}+\dfrac{1}{2!}-\dfrac{1}{3!}+\dfrac{1}{4!}\right)=24\left(\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{24}\right)=24\left(\dfrac{12-4+1}{24}\right)=9$$

D(1) = 0, D(2) = 1, D(3) = 2, D(4) = 9, D(5) = 44, and D(6) = 265

4. Arrangement with repetitions

If x items out of n items are repeated, then the number of ways of arranging these n items is $$\dfrac{n!}{x!}$$ ways. If x items, y items and z items are repeated within n items, they can be arranged in $$\frac{n!}{a!b!c!}$$ ways.

CAT probability and combinatorics questions are the important questions that frequently appear in the CAT examination. These questions require a solid understanding of fundamental concepts such as permutations, combinations, and probability distributions. As such, CAT aspirants need to grasp these topics to excel in the exam thoroughly. To help the aspirants, we have compiled all the questions from this topic that appear in the previous CAT papers, along with the video solutions for every question explained in detail by the CAT experts. One can download them in a PDF format or take them in a test format. Click on the link below to download the CAT probability and combinatorics questions with detailed video solutions PDF.