Probability Ke Sabse Important Formulas | Quick Revision

Описание: *🎯 Probability Tutorial – Deck of Cards & Dice | Class 11/12 Maths | JEE/NDA Prep*

This video covers a complete, step-by-step explanation of **Probability using Cards and Dice**, essential for school boards, JEE, NDA, CUET, and other competitive exams. Read below to revise key concepts anytime!

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🎴 DECK OF CARDS – STEP-BY-STEP GUIDE

*1. Total Cards in a Deck*

A standard deck has *52 cards* (no jokers)
Divided into **4 suits**:

Hearts (♥️) – Red
Diamonds (♦️) – Red
Clubs (♣️) – Black
Spades (♠️) – Black
Each suit has *13 cards*

*2. Types of Cards in Each Suit*

Number cards: 2 to 10 → 9 cards per suit
Face cards: Jack, Queen, King → 3 per suit
Ace → 1 per suit
Total face cards = 3 × 4 = *12*
Total number cards = 9 × 4 = *36*
Total aces = 4

*3. Colors in the Deck*

Red cards = 26 (Hearts + Diamonds)
Black cards = 26 (Clubs + Spades)

*4. Common Probability Questions*

Probability of Ace = 4/52 = *1/13*
Probability of red card = 26/52 = *1/2*
Probability of face card = 12/52 = *3/13*
Probability of Queen of Hearts = 1/52
Probability of red face card = 6/52 = *3/26*

*5. Summary Table*

| Category | Count |
| -------------- | ----- |
| Total Cards | 52 |
| Cards per Suit | 13 |
| Red Cards | 26 |
| Black Cards | 26 |
| Face Cards | 12 |
| Aces | 4 |

*Tip:*
Always check if the card is *replaced or not* in multi-card questions. Memorize key categories like total Kings (4), all Spades (13), red face cards (6), etc.

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🎲 DICE – STEP-BY-STEP GUIDE

*1. Dice Basics*

A standard die has **6 faces**, numbered 1 to 6
Each number has **equal probability**: 1/6
Dice questions can involve 1 die or 2 dice

*2. Single Dice Probability Examples*

Probability of getting 4 = 1/6
Probability of even number (2, 4, 6) = 3/6 = *1/2*
Probability of number greater than 3 (4, 5, 6) = 3/6 = *1/2*
Probability of getting prime number (2, 3, 5) = 3/6 = *1/2*

*3. Two Dice Basics*

Total outcomes = 6 × 6 = *36*
Each outcome is in form of (x, y) → where x and y are from 1 to 6

*4. Two Dice Probability Examples*

Sum = 7 → (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes → 6/36 = *1/6*
Sum = 2 → (1,1) → 1/36
Doubles (same number on both dice): (1,1), (2,2), … (6,6) → 6/36 = *1/6*
Sum greater than 10 → (5,6), (6,5), (6,6) → 3 outcomes → 3/36 = *1/12*

*5. Summary Table (Two Dice)*

| Event | Outcomes | Probability |
| -------------- | -------- | ----------- |
| Total Outcomes | 36 | - |
| Sum = 7 | 6 | 6/36 = 1/6 |
| Doubles | 6 | 6/36 = 1/6 |
| Sum = 2 or 12 | 1 each | 1/36 |

*Tip:*
In two-dice problems, *list all outcomes* for sums or conditions. Practice common sums like 7, 8, 10.
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