Dice

🎲 Dice – Basics of Probability

Dice is an important part of Probability Mathematics. It helps to calculate the probability of an event taking place.

📌 Definition

Calculating the probability of an event occurringProbabilityis

🎲 Information about Dice

• ✔ A Dice has 6 faces
• ✔ Numbers: 1, 2, 3, 4, 5, 6
• ✔ Total Results = 6

🧮 Key formula

Probability = Favorable outcomes / Total outcomes

💡 Example 1

What is the probability of getting 3 when throwing a dice?

Favorable = 1 (only 3) Total = 6

Probability = 1 / 6

💡 Example 2

Probability of even number (2,4,6)?

Favorable = 3 Total = 6

Probability = 3 / 6 = 1 / 2

💡 Example 3

Probability of getting odd number?

(1,3,5) → 3 outcomes Probability = 3 / 6 = 1 / 2

🔄 Key concepts

• ✔ Total outcomes = 6 (one Dice)
• ✔ Favorable outcomes count is important
• ✔ Probability value ranges from 0 to 1

📏 Important notes

• ✔ Probability = 0 → Impossible
• ✔ Probability = 1 → Certain
• ✔ Fraction should be simplified

Exams include “What is the Even/Prime number Probability when rolling a Dice?”, “What is two dice sum?” Questions like

🎲 Dice – Key formulas

🧮 1. Basic Formula of Probability

P(E) = Favorable Outcomes / Total Outcomes

🧮 2. Single Dice

• ✔ Total outcomes = 6
• ✔ Numbers = 1, 2, 3, 4, 5, 6

3. Two Dice

Total outcomes = 6 × 6 = 36

🧮 4. Complement Rule

P(E') = 1 - P(E)

🧮 5. Even / Odd

• ✔ Even numbers = 2, 4, 6 → 3 outcomes
• ✔ Odd numbers = 1, 3, 5 → 3 outcomes
• ✔ Probability = 3/6 = 1/2

🧮 6. Prime Numbers

• ✔ Prime = 2, 3, 5 → 3 outcomes
• ✔ Probability = 3/6 = 1/2

7. Sum (Two Dice)

• ✔ Sum = 7 → 6 outcomes
• ✔ Probability = 6/36 = 1/6

🧮 8. At least / At most

At least = ≥ (greater than or equal to) At most = ≤ (less than or equal)

📏 Important notes

• ✔ Probability value = 0 to 1
• ✔ Easy if you know total outcomes
• ✔ You can solve shortcut using Complement method
• ✔ Two dice → 36 combinations

🎲 Dice – 10 Examples + Shortcut Tricks

📘 Example 1

Probability of getting 4 when throwing a dice?

= 1 / 6

📘 Example 2

Probability of even number?

(2,4,6) → 3/6 =1/2

📘 Example 3

Probability of getting odd number?

(1,3,5) → 3/6 =1/2

📘 Example 4

Probability of getting prime number?

(2,3,5) → 3/6 =1/2

📘 Example 5

Probability to get above 6?

= 0 (Impossible)

📘 Example 6

A number less than 3 when rolling a dice?

(1,2) → 2/6 =1/3

📘 Example 7

When two dice are thrown sum = 7?

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6/36 =1/6

📘 Example 8

Two Dice sum = 10?

(4,6),(5,5),(6,4) → 3/36 =1/12

📘 Example 9

Probability of getting at least one 6?

Shortcut:1 - P(no 6)

= 1 - (5/6 × 5/6) = 1 - 25/36 =11/36

📘 Example 10

Probability of both dice coming even?

(3/6 × 3/6) = 9/36 =1/4

🚀 Shortcut Tricks

• ✔ 1 Dice → Total = 6
• ✔ 2 Dice → Total = 36
• ✔ At least → 1 - (No case)
• ✔ Even = 3, Odd = 3
• ✔ Prime = 3 (2,3,5)