Knowledge organisers

Probability: CBSE Class 11 Maths knowledge organiser

Everything to know about 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

Sample space: The set of all possible outcomes of a random experiment.
Mutually exclusive events: Events that cannot happen together: A ∩ B = φ.
Exhaustive events: Events that together cover the whole sample space.

Key formulas

Axioms: \(P(E)\ge0\), \(P(S)=1\), additive for mutually exclusive events	\(P(\text{not }A)=1-P(A)\)
Addition rule	\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(A\) but not \(B\); neither	\(P(A)-P(A\cap B);\) \(1-P(A\cup B)\)

Worked example

Two dice are thrown. Find \(P(\text{sum} = 5)\).

\((1,4), (2,3), (3,2), (4,1)\): \(\dfrac{4}{36} = \dfrac19\).

Common mistakes

Adding \(P(A) + P(B)\) for events that can happen together (the overlap is counted twice).
Listing unordered outcomes for two dice, which are not equally likely.
Assigning probabilities that are negative or do not add up to \(1\).
Confusing "mutually exclusive" (cannot both happen) with "exhaustive" (between them cover everything).

You should be able to…

Write sample spaces, describe 'not', 'and' and 'or' events and use P(not A) = 1 − P(A).
Use the addition rule, test assignments against the axioms and count with combinations.
Solve multi-part problems with dice, cards, committees and survey data.
Combine mutually exclusive cases and complements in less direct questions.

The printable sheet

Probability knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Probability knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · All CBSE Class 11 Maths organisers