Knowledge organisers

Introduction to Probability: CBSE Class 9 Maths knowledge organiser

Everything to know about introduction to probability on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Experiment: An action with outcomes that can be observed, such as tossing a coin.
Event: A set of outcomes of an experiment.
Probability: A number from 0 to 1 showing how likely an event is.

Key formulas

Experimental	\(P(E)=\frac{\text{trials with }E}{\text{total trials}}\)
Theoretical (equally likely)	\(P(E)=\frac{\text{favourable}}{\text{total}};\) \(P(\text{not }E)=1-P(E)\)
\(0\le P\le1\); tree diagram: one branch per stage; two coins 4, coin + die 12, two dice 36 outcomes

Worked example

A fair die is thrown. Find the probability of a number greater than \(4\).

Favourable \(\{5, 6\}\): \(P = \dfrac26 = \dfrac13\).

Common mistakes

Listing two coins as \(\{2H, 1H, 0H\}\): these are not equally likely; list \(HT\) and \(TH\) separately.
Using the theoretical value when the question asks for the experimental probability from data.
Probabilities greater than \(1\) or negative: check every answer lies in \([0, 1]\).
Counting an outcome twice (for example \(15\) as both a multiple of \(3\) and of \(5\)).

You should be able to…

Place events on the probability scale and find simple experimental and theoretical probabilities.
List sample spaces for coins, dice and spinners, use data tables and estimate expected frequencies.
Use tree diagrams and solve multi-part problems on bags, spinners and recorded data.
Handle two-dice and two-spinner events such as 'the first number is larger' or 'sum greater than product'.

The printable sheet

Introduction to Probability knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Introduction to Probability knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · All CBSE Class 9 Maths organisers