Questions
2–4 questions per paper
Difficulty
Medium
Importance
Medium yield, high scoring potential
Overview
Probability and Permutation-Combination form the bedrock of quantitative reasoning in PSU entrance exams, testing your ability to analyze uncertainty and logical arrangements. Mastering these topics is essential because they frequently appear in data interpretation sets and logical reasoning sections, often serving as the differentiator between qualified and non-qualified candidates.
Permutations and Combinations
Permutations focus on the order of arrangements, while combinations prioritize the selection of items regardless of order. Understanding the fundamental counting principle is the starting point for solving complex selection problems.
- Permutation formula: nPr = n! / (n-r)!
- Combination formula: nCr = n! / [r!(n-r)!]
- Circular permutation: (n-1)!
- Selection of r items from n: nCr
- Arrangement of identical items: n! / (p!q!r!)
Basic Probability
Probability is defined as the ratio of favorable outcomes to the total number of equally likely outcomes in a sample space. This concept forms the foundation for all complex probabilistic modeling in competitive exams.
- P(A) = Favorable Outcomes / Total Outcomes
- Range of probability: 0 <= P(A) <= 1
- Sum of all probabilities in a sample space = 1
- P(not A) = 1 - P(A)
- Probability of A or B: P(A U B) = P(A) + P(B) - P(A ∩ B)
Conditional Probability and Bayes Theorem
Conditional probability measures the likelihood of an event occurring given that another event has already occurred. Bayes' Theorem is the standard tool for revising existing predictions based on new evidence.
- P(A|B) = P(A ∩ B) / P(B)
- Multiplication rule: P(A ∩ B) = P(A) * P(B|A)
- Bayes' Theorem: P(A|B) = [P(B|A) * P(A)] / P(B)
- Independent events: P(A ∩ B) = P(A) * P(B)
- Mutually exclusive events: P(A ∩ B) = 0
Formula Sheet
nPr = n! / (n-r)!
nCr = n! / (r!(n-r)!)
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A|B) = P(A ∩ B) / P(B)
Bayes Theorem: P(Hi|E) = [P(E|Hi) * P(Hi)] / Summation(P(E|Hj) * P(Hj))
Exam Tip
Always identify if the problem involves selection (Combination) or arrangement (Permutation) before calculating, as this distinction is the most common point of failure.
Common Mistakes
- Confusing Permutations with Combinations when the order of elements actually matters in the final arrangement.
- Forgetting to subtract the intersection of events when calculating the union of two non-mutually exclusive sets.
- Applying the independence assumption for events when the problem context implies dependence.
More Revision Notes
Ready to test yourself?
Play topic-wise Probability & Permutation-Combination questions in Aspirant Arcade — gamified MCQ practice.
Download Free