Class 10 Maths Chapter 14: Probability Concept Infographic (NCERT)

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Chapter 14: Probability

Theoretical Probability, Complementary Events, and Deck of Cards Masterclass[cite: 14].

🎲 Theoretical Probability

Also called classical probability, formulated by Pierre Simon Laplace (1795)[cite: 14].

P(E) =

Number of outcomes favourable to ENumber of all possible outcomes

[cite: 14]

Golden Rule of Probability:
The probability of any event P(E) always lies between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1[cite: 14].

🔄 Complementary Events

The event E (not E) represents the complement of event E[cite: 14].

P(E) + P(E) = 1  ⇒  P(E) = 1 - P(E)

Sure vs Impossible Events:
• Probability of a sure event = 1[cite: 14].
• Probability of an impossible event = 0[cite: 14].

🃏 The 52 Playing Cards Anatomy

Standard deck of cards is divided equally into 4 suits of 13 cards each[cite: 14].

🔴 Red Cards (26)

Hearts (♥): 13 cards
Diamonds (♦): 13 cards[cite: 14]

⚫ Black Cards (26)

Spades (♠): 13 cards
Clubs (♣): 13 cards[cite: 14]

👑 Face Cards (12)

4 Kings, 4 Queens, 4 Jacks
(6 Red face cards, 6 Black face cards)[cite: 14]

⭐ Board Exam Super-Hacks

Two Dice Sample Space Trick

When throwing two dice simultaneously, total possible outcomes = 6 × 6 = 36[cite: 14]. For a sum of 8, look for pairs: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes → Probability = 5/36[cite: 14].

Sum of Elementary Probabilities

The sum of the probabilities of all the elementary events (events with a single outcome) of an experiment is always 1[cite: 14].

⚠️ Common Exam Traps

Trap 1: Probability Greater than 1

If your calculated probability is greater than 1 (e.g., 3/2) or negative (e.g., -1.5), your answer is mathematically wrong. Probability can NEVER exceed 1 or be negative[cite: 14]!

Trap 2: Card Drawing Without Replacement

If a card/ball/pen is drawn and NOT replaced, remember to reduce the total number of outcomes (denominator) by 1 for the next draw (e.g., from 52 to 51 cards)[cite: 14]!

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