Chapter 7: The Mathematics of Maybe: Introduction to ProbabilityClass 9 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

This chapter introduces probability as a measure of how likely a random event is to occur, on a scale from \(0\) (impossible) to \(1\) (certain), with \(0 \le P(E) \le 1\). Randomness means the outcome of an experiment such as tossing a coin or rolling a die cannot be predicted, though all possible outcomes are known. There are two objective ways to estimate probability. Experimental probability uses data: \(\dfrac{\text{number of times the event occurred}}{\text{total number of trials}}\), also called relative frequency. Theoretical probability assumes equally likely outcomes: \(\dfrac{\text{number of favourable outcomes}}{\text{number of possible outcomes}}\). By the Law of Large Numbers, experimental probability tends toward the theoretical value as trials increase. The chapter warns against the Gambler's Fallacy, since each trial is independent and has no memory. The sample space \(S\) is the set of all outcomes, its size \(n(S)\), and an event is a subset of \(S\). Tree diagrams list and find probabilities of outcomes in multi-step experiments. Statistical sampling estimates population proportions from a representative sample.

Key terms

Extra questions & answers

Exercise Set 7.1

Exercise Set 7.2

Exercise Set 7.3

Exercise Set 7.4

End-of-Chapter Exercises

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