Class 10 · Chapter 14

Probability

Classical (theoretical) probability, sample space, favourable outcomes, complementary events.

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Mathematics · Class 10 (2026-27)

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Detailed theory

A random experiment has more than one possible outcome, and it is not possible to predict the outcome in advance. E.g. tossing a coin (outcomes: H, T), rolling a die (1–6), drawing a card. The sample space

S

is the set of all possible outcomes.

Key concepts & formulas

P(E) = \dfrac{\text{number of favourable outcomes}}{\text{total outcomes}}

0 \le P(E) \le 1

P(E) + P(\bar E) = 1

Sum of probabilities of all outcomes in the sample space

= 1

P(\text{impossible}) = 0

;

P(\text{sure}) = 1

For equally likely outcomes, use the classical formula.