Chapter 14 · Class X Mathematics · NCERT Exercises

Probability — Exercises

Classical Probability — All 30 Probability Problems Fully Solved

📂 1 Exercise 📝 25 Questions 🎓 Easy-Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 14.1

Theoretical probability; coins, dice, cards, balls; complement events

25 Q Easy-Moderate

1 exercise file · 25 total questions

Chapter at a Glance

CBSE BoardsNTSE

7 Concepts

5 Formulas

Easy-Moderate Difficulty

5–7% Weightage

Before You Begin

Prerequisites

✓Permutations & combinations intuition
✓Sets (for event notation)
✓Basic fraction simplification

Have Ready

🔧Sample space listing grid
🔧Standard playing card diagram (52 cards breakdown)
🔧Tree diagram template

Exercise Topic Map

Exercise 14.1 P(E) = n(favourable outcomes)/n(total outcomes); list sample space for small experiments; complement P(Ē) = 1 − P(E)

Key Formulae — Recall Before Solving

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

\(P(\bar{E}) = 1 - P(E)\)

\(P(E) + P(\bar{E}) = 1\)

\(\text{Impossible event: }P = 0;\quad \text{Sure event: }P = 1\)

NCERT Solving Method

Step 1 — Always list n(S) first: count total equally-likely outcomes. Step 2 — Identify favourable outcomes carefully; list them out for small sample spaces. Step 3 — Cards: memorise structure — 52 cards, 4 suits (13 each), 3 face cards per suit (Jack, Queen, King). Step 4 — Complement: P(at least one) = 1 − P(none); P(at most one) = 1 − P(two or more). Step 5 — Express answer as simplified fraction; verify 0 ≤ P ≤ 1.