📖 Chapter 14 — Probability (CBSE Class 10 Maths): Detailed notes — theoretical (classical) probability, with coins, dice, cards and bags.
Chapter 14 — Probability
🎲 1. Theoretical (Classical) Probability
P(E) = (Number of favourable outcomes) / (Total number of outcomes)
This assumes all outcomes are equally likely.
📏 2. Important Facts
- 0 ≤ P(E) ≤ 1 — probability is never negative and never more than 1.
- P(E) + P(not E) = 1, so P(not E) = 1 − P(E).
- Probability of an impossible event = 0; of a sure (certain) event = 1.
- The sum of the probabilities of all elementary events of an experiment = 1.
🃏 3. Common Totals
- One coin → 2 outcomes (H, T). Two coins → 4 (HH, HT, TH, TT).
- One die → 6 outcomes (1–6).
- A deck → 52 cards (26 red + 26 black; 4 suits of 13; 4 aces, 4 kings, 12 face cards).
🧠 Remember: P(E) = favourable/total. 0 ≤ P ≤ 1. P(not E) = 1 − P(E). Impossible = 0, sure = 1. Deck: 52 cards, 4 of each rank, 13 of each suit, 12 face cards. Probability can never be negative or > 1.
⭐ Exam Tips: ① Count total & favourable outcomes carefully. ② P(not E) = 1 − P(E). ③ Cards: know the counts (aces, kings, red/black, face). ④ Dice/coins: list the sample space. ⑤ A value like −1.5 or 1.3 can NEVER be a probability.