Chapter 7 — The Mathematics of Maybe: Introduction to Probability

Chapter 7 of the Class 9 Maths NCERT textbook, "The Mathematics of Maybe: Introduction to Probability", introduces probability as a measure of how likely a random event is, scaled from 0 (impossible) to 1 (certain), covering experimental and theoretical probability, sample spaces, events, and tree diagrams.

• Measuring Likelihood — Probability puts a number on how likely an event is, on a scale from 0 (impossible) to 1 (certain). Random experiments like tossing a coin have known outcomes that remain individually unpredictable.
• Two Ways to Find Probability — Experimental probability divides how often an event occurred by the number of trials, while theoretical probability divides favourable outcomes by all equally likely possible outcomes.
• Sample Spaces and Events — The sample space S lists every possible outcome, and an event is a subset of it. Tree diagrams map out all outcomes of multi-step experiments like tossing two coins.
• Long-Run Behaviour — The Law of Large Numbers describes how results settle over many trials, while the Gambler's Fallacy warns against expecting past outcomes to influence future random ones.

1. 01Probability measures likelihood on a scale from 0 (impossible) to 1 (certain)
2. 02Randomness means outcomes are known but each result is unpredictable
3. 03Experimental probability = times event occurred / total number of trials
4. 04Theoretical probability P = favourable outcomes / possible outcomes
5. 05Sample space S lists all possible outcomes; n(S) is the sample size
6. 06An event is a subset of the sample space
7. 07Tree diagrams list all outcomes of multi-step experiments like tossing two coins
8. 08The Law of Large Numbers and Gambler's Fallacy explain long-run behaviour