Probability – Class 10 Maths Chapter 14: Theoretical Probability & Solved Examples

Chapter 14: Probability

14.1 Theoretical (Classical) Probability

14.2 Key Terms

• Experiment: An action that produces well-defined outcomes (e.g., tossing a coin, rolling a die).
• Sample Space: The set of all possible outcomes. For a die: S = {1, 2, 3, 4, 5, 6}.
• Event: A subset of the sample space. E.g., "getting an even number" = {2, 4, 6}.
• Complementary Event: If E is an event, then Ē (not E) is the complementary event.

14.3 Common Probability Problems

Tossing Coins

• 1 coin: Sample space = {H, T}, total outcomes = 2
• 2 coins: Sample space = {HH, HT, TH, TT}, total outcomes = 4
• 3 coins: Total outcomes = 8
• n coins: Total outcomes = 2ⁿ

Rolling Dice

• 1 die: Total outcomes = 6
• 2 dice: Total outcomes = 36
• P(sum = 7 on two dice) = 6/36 = 1/6 (the most likely sum)

Playing Cards (Standard Deck of 52)

• 4 suits: Spades ♠ (13), Hearts ♥ (13), Diamonds ♦ (13), Clubs ♣ (13)
• Red cards: Hearts + Diamonds = 26; Black cards: Spades + Clubs = 26
• Face cards: Jack, Queen, King = 4 × 3 = 12 total
• Aces: 4 total (one per suit)

14.4 Solved Examples

Example 1: A bag contains 3 red, 5 blue, and 2 green balls. A ball is drawn at random. Find P(not green).

Solution

Total balls = 3 + 5 + 2 = 10

P(green) = 2/10 = 1/5

P(not green) = 1 − 1/5 = 4/5

Example 2: Two dice are thrown simultaneously. Find the probability that the sum is greater than 10.

Solution

Total outcomes = 36

Favourable outcomes (sum > 10): (5,6), (6,5), (6,6) → sum=11 or 12

Number of favourable outcomes = 3

P(sum > 10) = 3/36 = 1/12

Example 3: A card is drawn from a well-shuffled deck. Find P(face card).

Solution

Total cards = 52, Face cards = 12 (4 Jacks + 4 Queens + 4 Kings)

P(face card) = 12/52 = 3/13