Schooling · Class 10 · Mathematics · Probability · Chapter on a page
CBSE Class 10 · Mathematics · NCERT Mathematics
Probability: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A random experiment is an action…
- The sample space is the set of all…
- An event is any subset of the sample…
- Equally likely outcomes are outcomes…
- The probability of an event equals…
- A certain event has probability 1…
- The sum of probabilities of an event…
- Formulas and facts
- Probability of an event E
- This gives the likelihood of event E…
- Probability of complement
- If you know the chance of something…
- Range of probability
- Probability is never negative and…
- Certain event
- Watch out for
- Counting outcomes incorrectly when…
- Forgetting that probability cannot…
- Confusing favourable outcomes with…
- Assuming dice or coins are fair…
- Adding probabilities of overlapping…
What this chapter is about
Probability is the branch of mathematics that measures how likely an event is to happen. In earlier classes, you explored probability through experiments and observations. In Class 10, you study the theoretical approach, where you calculate probability without actually performing the experiment, using logical reasoning about equally likely outcomes.
Key ideas
- A random experiment is an action where the outcome cannot be predicted with certainty, but all possible outcomes are known in advance.
- The sample space is the set of all possible outcomes of an experiment. For a single die roll, the sample space is {1, 2, 3, 4, 5, 6}.
- An event is any subset of the sample space; it consists of one or more outcomes we are interested in.
- Equally likely outcomes are outcomes that have the same chance of occurring, such as getting heads or tails in a fair coin toss.
- The probability of an event equals the number of favourable outcomes divided by the total number of outcomes, when outcomes are equally likely.
- A certain event has probability 1, and an impossible event has probability 0.
- The sum of probabilities of an event and its complement (the event not happening) is always 1.
- Probability of any event lies between 0 and 1, inclusive: 0 ≤ P(E) ≤ 1.
Formulas and facts to remember
- Probability of an event E:P(E) = Number of favourable outcomes / Total number of outcomes
- This gives the likelihood of event E occurring when all outcomes are equally likely.
- Probability of complement:P(not E) = 1 − P(E)
- If you know the chance of something happening, subtract from 1 to find the chance of it not happening.
- Range of probability:0 ≤ P(E) ≤ 1
- Probability is never negative and never exceeds 1.
- Certain event:P(E) = 1 when E always happens.
- Impossible event:P(E) = 0 when E can never happen.
- Sample space for common experiments:
- One coin: {H, T} — 2 outcomes
- Two coins: {HH, HT, TH, TT} — 4 outcomes
- One die: {1, 2, 3, 4, 5, 6} — 6 outcomes
- Two dice: 36 outcomes (each die independent)
- Standard deck of cards: 52 cards (13 each of 4 suits)
Common mistakes
- Counting outcomes incorrectly when two coins are tossed by treating HT and TH as the same → Treat them as distinct; order matters, giving 4 outcomes, not 3.
- Forgetting that probability cannot exceed 1 → If your answer is greater than 1, recheck your count of favourable and total outcomes.
- Confusing favourable outcomes with unfavourable ones when using the complement rule → P(not E) = 1 − P(E), so subtract the event's probability, not add.
- Assuming dice or coins are fair without checking the problem statement → Read carefully; some problems state biased coins or loaded dice.
- Adding probabilities of overlapping events directly → When events share outcomes, use the addition rule carefully or count overlapping outcomes once.
Quick revision
- Probability = Favourable outcomes / Total outcomes (for equally likely outcomes).
- P(E) + P(not E) = 1; use this to find one if the other is known.
- Sample space for one die has 6 outcomes; for two dice, 36 outcomes.
- A standard deck has 52 cards: 4 suits, 13 cards each.
- Probability is always between 0 and 1, inclusive.
- List all outcomes carefully before counting; missed outcomes cause errors.