Knowledge organisers

Probability: CBSE Class 10 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

Theoretical probability: Favourable outcomes ÷ total outcomes, when all outcomes are equally likely.
Complementary events: E and 'not E': P(E) + P(not E) = 1.
Sure and impossible events: A sure event has probability 1; an impossible event has probability 0.

Key formulas

Classical probability	\(P(E)=\frac{\text{favourable outcomes}}{\text{total outcomes}}\)
Complement; range	\(P(E)+P(\bar E)=1;\) \(0\le P(E)\le1\)
Sure event 1, impossible event 0; probabilities of all elementary events add to 1
Cards: 52 = 4 suits × 13; 26 red, 26 black; 12 face cards. Two dice: 36 outcomes

Worked example

Two dice are thrown. Find the probability that the sum is 9. Favourable: (3,6), (4,5), (5,4), (6,3), so \(P=\frac{4}{36}=\frac19\).

Common mistakes

Treating "HT" and "TH" as one outcome, or listing (2,3) but not (3,2) for two dice.
Forgetting that 1 is neither prime nor composite.
Counting 16 face cards (the aces are not face cards).
Not reducing the fraction, or giving a probability greater than 1.

You should be able to…

You know that probabilities lie between 0 and 1, can use P(not E) = 1 − P(E), and can find simple probabilities.
List outcomes for coins, dice and cards correctly and solve the standard board questions on each.
Write complete long answers and case studies, listing favourable outcomes and giving answers in lowest terms.
Handle two-dice products and sums, modified card packs and 'find the number of balls' problems.

The printable sheet

Probability knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Probability knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · All CBSE Class 10 Maths organisers