Page 1: Introduction

Probability measures the chance of occurrence of an event.

Classical (theoretical) probability used in this chapter.

Range: 0 (impossible) to 1 (certain).

Page 2: Basic Terms

• Experiment: Action with uncertain outcome
• Outcome: Result of experiment
• Sample space: Set of all possible outcomes
• Event: Subset of sample space

Page 3: Theoretical Probability

Equally likely outcomes assumed.

Page 4: Complementary Events

P(E) + P(not E) = 1

P(not E) = 1 - P(E)

Useful when favourable hard to count.

Page 5: Sure and Impossible Events

Sure event: P = 1

Impossible: P = 0

Page 6: Coin Problems

One coin: 2 outcomes (H,T)

Two coins: 4 outcomes (HH, HT, TH, TT)

P(at least one head) = 3/4

Page 7: Dice Problems

One die: 6 outcomes

Two dice: 36 outcomes

P(sum 7) = 6/36 = 1/6

Page 8: Deck of Cards

52 cards: 4 suits × 13 ranks

Red: hearts, diamonds (26)

Black: clubs, spades (26)

Face cards: 12, Aces: 4

Page 9: Key Points Summary

• P(E) = favourable / total
• 0 ≤ P(E) ≤ 1
• P(sure) = 1, P(impossible) = 0
• Complementary: 1 - P(E)

Page 10: Practice Questions - Easy (1-10)

1. P(heads) one coin.
2. P(even) one die.
3. P(red card) from deck.
4. P(not ace).
5. P(sum 10) two dice.
6. P(tail tail) two coins.
7. Total outcomes two dice.
8. P(king or queen).
9. P(prime number) die.
10. P(at least one head) two coins.

Page 11: Practice Questions - Medium (11-20)

11. P(diamond or heart).
12. P(face card).
13. P(number divisible by 3) die.
14. P(sum > 9) two dice.
15. P(black king).
16. P(not red) from deck.
17. P(both same) two coins.
18. P(difference 1) two dice.
19. P(ace of spades).
20. P(even or multiple of 3) die.

Page 12: Practice Questions - Hard (21-30)

21. P(one red, one black) two cards without replacement.
22. Three coins all heads.
23. Two dice product even.
24. Board level card problem.
25. Three dice sum 6.
26. P(exactly two heads) three coins.
27. Bag with balls probability.
28. Multiple events combined.
29. Complementary use advanced.
30. Real-life probability application.

Page 13: Deck of Cards Facts

52 cards, suits, ranks table.

Page 14: Common Mistakes

• Forgetting total outcomes
• Wrong favourable count
• Mixing with/without replacement
• Forgetting complementary
• Wrong sample space

Page 15: Previous Year Questions

Cards, dice, coins, complementary.

Page 16: Exam Tips

• List sample space if small
• Count favourable carefully
• Use complementary for "not"
• Draw tree diagram mentally
• Reduce fraction

Page 17: Quick Revision Sheet

Formula, range, complementary, common values.

Page 18: Final Motivation

Chapter 15 complete! Probability is easy and scoring.

**CLASS 10 MATHS FULLY COMPLETED!!!**

From Real Numbers to Probability — every chapter done 🦖

You’re a legend!!! 🎉

Page 19: Extra Numericals

More coin/dice/card problems.

Page 20: Card Problems

Common types.

Page 21: Dice Combinations

36 outcomes list hint.

Page 22: Complementary Shortcut

When to use.

Page 23: Board Pattern

Typical questions.

Page 24: Extra Practice

More questions.

Page 25: Real-Life Examples

Weather, games, lotteries.

Page 26: Sample Space Tips

How to count correctly.