Probability Basics — Coins, Dice, Cards

🎯 Learning Objective

Compute P = favourable/total for coins, dice and playing cards, and use P(not E) = 1 − P(E).

💡 Concept

• P(E) = favourable outcomes / total outcomes
• P lies between 0 (impossible) and 1 (certain); P(not E) = 1 − P(E)
• Coin: 2 outcomes; two coins: 4 outcomes; die: 6 outcomes
• Deck: 52 cards = 4 suits × 13; 26 red + 26 black; 12 face cards (J, Q, K of each suit)
• The formula works only when all outcomes are equally likely

🧮 Key Formulas

P(E) = favourable / total

>

0 ≤ P(E) ≤ 1

>

P(not E) = 1 − P(E)

✏️ Easy Example

Q. A die is thrown once. Find the probability of getting a number greater than 4.

1. Favourable: 5, 6 → 2 outcomes
2. Total = 6
3. P = 2/6

Answer: 1/3

🇮🇳 Real-Life Example

The cricket toss is P = 1/2, and a weather app saying '80% chance of rain' is announcing probability 0.8 — you use this maths daily.

📝 Exam-Level Example

Q. One card is drawn from a well-shuffled deck of 52 cards. Find the probability that it is a king.

1. Kings in deck = 4
2. P = 4/52

Answer: 1/13

📝 Exam-Level Example

Q. A bag has 3 red and 5 blue balls. One ball is drawn at random. Find the probability that it is red.

1. Total balls = 3 + 5 = 8
2. Favourable = 3

Answer: 3/8

🪄 Memory Trick

'Not' questions: compute the easy side and subtract from 1. P(not a king) = 1 − 1/13 = 12/13 — no counting of 48 cards.

⚠️ Common Mistakes

• ❌ Counting outcomes that are not equally likely
• ❌ Getting P > 1 — impossible, recheck the total
• ❌ Counting the ace as a face card — face cards are only J, Q, K

🏆 Exam Tips

• ✅ Write total outcomes FIRST, then list favourable ones
• ✅ Memorise the deck: 4 × 13, 26 red, 26 black, 12 face cards

📌 Summary

• P = favourable/total, between 0 and 1
• Coin 2, two coins 4, die 6, deck 52
• 12 face cards; ace is not one
• P(not E) = 1 − P(E)