Probability
🟢 Lite — Quick Review (1h–1d)
Rapid summary for last-minute revision.
Probability — Key Facts for CUET
• Essential Formula: P(A) = (Number of favorable outcomes)/(Total outcomes). For complementary events: P(A’) = 1 - P(A). For union of two events: P(A∪B) = P(A) + P(B) - P(A∩B) • Most Tested CUET Concept: Conditional probability and Bayes’ theorem, often applied to real-world scenarios like medical tests or quality control • Common Mistake Students Make: Assuming events are mutually exclusive when they aren’t, leading to incorrect use of addition rule without subtracting intersection • Key Technique: Draw Venn diagrams or probability trees for complex problems. For “at least one” problems, use complement: P(at least one) = 1 - P(none) • Important Exception: When events are independent, P(A∩B) = P(A) × P(B). Don’t confuse independence with mutually exclusive (these are opposite concepts) • Most Frequent Question Type: Probability involving dice, cards, balls drawn from bags, and questions using Bayes’ theorem with two or three scenarios ⚡ Exam tip: In “without replacement” problems, remember probabilities change after each draw. Use hypergeometric distribution or sequential multiplication for accuracy.
🟡 Standard — Regular Study (2d–2mo)
Standard content for students with a few days to months.
Probability — CUET Study Guide
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. The foundation lies in counting outcomes using permutations and combinations.
Key Formulas:
- Classical Probability: P(E) = n(E)/n(S), where n(E) is favorable outcomes and n(S) is total outcomes
- Conditional Probability: P(A|B) = P(A∩B)/P(B)
- Bayes’ Theorem: P(A|B) = [P(B|A) × P(A)] / P(B)
- Multiplication Rule: P(A∩B) = P(A) × P(B|A)
- Total Probability: P(B) = Σ P(B|Aᵢ) × P(Aᵢ)
Typical CUET Patterns: Questions often involve drawing cards from a deck, rolling dice, selecting balls from bags (with/without replacement), or applying Bayes’ theorem to real-life scenarios like disease testing or quality inspection.
Common Traps:
- Forgetting to subtract intersection when using addition rule
- Treating dependent events as independent
- Misidentifying “or” versus “and” in problem statements
Example 1: Two dice are thrown. Find probability of getting sum 8. Solution: Total outcomes = 36. Favorable pairs: (2,6),(3,5),(4,4),(5,3),(6,2) = 5. P = 5/36.
Example 2: A bag contains 3 red and 5 blue balls. Two balls drawn without replacement. Find P(both red). Solution: P = (3/8) × (2/7) = 6/56 = 3/28.
🔴 Extended — Deep Study (3mo+)
Comprehensive coverage for students on a longer timeline.
Probability — Comprehensive CUET Notes
Advanced Theory and Proofs:
Random Experiments and Sample Spaces: A random experiment has multiple possible outcomes. The sample space S contains all possible outcomes. An event is a subset of S.
Axiomatic Approach (Kolmogorov’s Axioms):
- P(A) ≥ 0 for any event A Content adapted based on your selected roadmap duration. Switch tiers using the pill selector above.