Chapter 14 · Class XI Mathematics · NCERT Exercises

Probability — Exercises

From Sample Spaces to Compound Events — All Probability Exercises Solved

📂 3 Exercises 📝 33 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

Sample space; events; subset relations between events

Axiomatic approach; probability of events; equally likely outcomes

Odds; P(AUB); conditional probability preview; word problems

3 exercise files · 33 total questions

Chapter at a Glance

JEE MainCBSE BoardsBITSATKVPY

11Concepts

12Formulas

ModerateDifficulty

5–7%Weightage

Before You Begin

Prerequisites

✓Sets (Ch 1) — for event notation
✓Permutations & Combinations (Ch 6) — for counting
✓Logical reasoning

Have Ready

🔧Tree diagram template
🔧Sample space listing grid
🔧Venn diagram for events

Exercise Topic Map

Exercise 14.1Write sample space S; list events as subsets; identify impossible event ∅

Exercise 14.2P(E)=n(E)/n(S) for equally likely; verify 0≤P(E)≤1; P(S)=1

Exercise 14.3P(A'́)=1−P(A); P(A∪B)=P(A)+P(B)−P(A∩B); mutually exclusive: P(A∩B)=0

MiscellaneousOdds in favour = P(E)/P(E'); combined experiments; card/dice problems

Key Formulae

\(P(E) = \dfrac{n(E)}{n(S)},\quad 0 \leq P(E) \leq 1\)

\(P(E') = 1 - P(E)\)

\(P(A \cup B) = P(A)+P(B)-P(A \cap B)\)

\(A,B\text{ mutually exclusive} \Rightarrow P(A \cup B)=P(A)+P(B)\)

NCERT Solving Method

Step 1 — Always write out the sample space S explicitly for small experiments. Step 2 — Identify the event E as a subset of S; count n(E) and n(S). Step 3 — For compound events: use addition theorem; never add probabilities without checking if mutually exclusive. Step 4 — Odds: odds in favour = m:(n−m) where P(E)=m/n. Step 5 — Multi-step experiments (cards, dice twice): use systematic listing or combinations.

Continue Your Preparation

📖 Notes Theory & concepts 🧠 MCQs Topic-wise practice 🎯 PYQs JEE · CBSE · BITSAT ⚖️ True–False Topic-wise concept check ➡️ Next Chapter Back to Chapter 1 — Sets

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