CBSE · Class 6-12

Class 10 · Mathematics (Standard)

Unit 14 · Class 10Mathematics (Standard)

Probability

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

Lessons

6 concepts

1
Random Experiments and Outcomes
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…
2
Event and Favourable Outcomes
An event $E$ is a subset of $S$ . If $E$ has $k$ favourable outcomes out of $n$ equally likely outcomes, then $P(E) = k/n$ . E.g. rolling an even number on a die: $E = \{2,4,6\}$ , $P(E) = 3/6 = 1/2$ .
3
Complementary Events
$\bar E$ (complement of $E$ ) is the event that $E$ does not occur. $P(E) + P(\bar E) = 1$ , so $P(\bar E) = 1 - P(E)$ . Complements often simplify: 'at least one head in 3 tosses' is easier as $1 - P(\text{no heads})$ .
4
Card Problems
A standard deck has $52$ cards: $4$ suits (hearts, diamonds, clubs, spades) of $13$ each. Face cards: J, Q, K ( $12$ total; $6$ red). Aces are usually counted separately. Common events: single suit, face card, red/black c…
5
Coin and Die Problems
$n$ coins tossed: $2^n$ outcomes. $n$ dice rolled: $6^n$ outcomes. To count outcomes matching a condition (e.g. exactly $k$ heads), use combinatorial reasoning: list or use $\binom{n}{k}$ . Fairness assumption is critical…
6
Bounds and Interpretation
Probabilities always lie in $[0, 1]$ . $P = 0$ means impossible; $P = 1$ means certain. Probabilities close to $0$ or $1$ are called rare or nearly certain events, respectively. Never assign a probability outside this ran…

Skills to practise

Skill · medium

Probability — Practice