Chapter 14 — Probability

Chapter 14 of the Class 10 Maths NCERT textbook, "Probability", introduces theoretical (classical) probability, defined as the number of outcomes favourable to an event divided by the total number of equally likely outcomes, with every probability lying between 0 and 1 inclusive.

• The classical definition — Theoretical probability assumes all outcomes are equally likely and measures an event as the fraction of outcomes that favour it. Every such probability sits between 0 and 1.
• Sure, impossible, and complementary events — An impossible event has probability 0 and a certain one has probability 1. For an event and its complement the probabilities add to 1, so knowing one gives the other.
• Applying it to experiments — These rules are worked through familiar experiments — coins, dice, cards, and marbles. For instance, two dice give 36 equally likely outcomes, and a deck of 52 cards makes such counting concrete.

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