Chapter 14 — Probability

Chapter 14 of NCERT Class 10 Mathematics introduces theoretical (classical) probability, defined as the number of outcomes favourable to an event divided by the total number of equally likely possible outcomes, with probability values always lying between 0 and 1 inclusive.

NCERT Class 10 Maths Chapter 14 covers theoretical probability, also called classical probability, introduced by Pierre Simon Laplace in 1795. It defines P(E) as the ratio of favourable outcomes to total equally likely outcomes. Key concepts include impossible events (probability 0), sure events (probability 1), elementary events, complementary events where P(E) + P(not E) = 1, and the rule that the sum of probabilities of all elementary events equals 1. The chapter applies these ideas to coins, dice, playing cards, marbles, and two-dice experiments.

1. 01Theoretical probability P(E) = (Number of outcomes favourable to E) / (Number of all possible outcomes), assuming equally likely outcomes
2. 02Probability of any event E satisfies 0 ≤ P(E) ≤ 1; an impossible event has probability 0 and a sure (certain) event has probability 1
3. 03For complementary events E and not-E: P(E) + P(not E) = 1, so P(not E) = 1 – P(E)
4. 04The sum of probabilities of all elementary events of an experiment is always 1
5. 05A standard deck has 52 cards in 4 suits of 13 each; probability of drawing an ace is 4/52 = 1/13
6. 06When two dice are thrown simultaneously, the total number of equally likely outcomes is 6 × 6 = 36