What is covered in Grade 11 Mathematics Probability?

Venn diagrams, addition and complementary rules. Mutually exclusive and independent events. Contingency tables.

Is Grade 11 Probability tested in Paper 1 or Paper 2?

Grade 11 Mathematics Probability is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Probability taught in Grade 11 Mathematics?

Probability is taught in Term 4 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Probability on the CAPS curriculum?

Yes. Probability is part of the official CAPS Mathematics curriculum for Grade 11, Term 4 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 4Mathematics

Probability

We extend Grade 10 probability to include conditional probability, the multiplication rule, and independent events.

Week 3

10.1 Conditional Probability & Independent Events

Apply conditional probability: $P(A|B)=\frac{P(A\cap B)}{P(B)}$
Apply the multiplication rule
Test for independence: $P(A\cap B)=P(A)\cdot P(B)$
Use contingency tables and tree diagrams

🌍

Real-World Connection

Medical testing uses conditional probability constantly. If a disease affects 1% of the population and a test is 99% accurate, the probability that a positive test result means you actually have the disease is NOT 99% — conditional probability gives the true answer, which surprises most people.

Conditional Probability

P(A|B) = \frac{P(A\cap B)}{P(B)}

$P(A|B)$ = probability of $A$ given $B$ has occurred; $P(B)>0$

Multiplication Rule

P(A\cap B) = P(A|B)\cdot P(B) = P(B|A)\cdot P(A)

Rearrangement of conditional probability

Property / Rule

Independent Events

Events $A$ and $B$ are independent if knowing $B$ occurred does NOT affect the probability of $A$ . Test: $P(A\cap B)=P(A)\cdot P(B)$ , equivalently $P(A|B)=P(A)$ .

P(A\cap B)=P(A)\cdot P(B)\Leftrightarrow A,B\text{ independent}

🚨 Common Mistake

Independent ≠ Mutually Exclusive! Mutually exclusive events CANNOT both occur; independent events CAN both occur (their joint probability is just the product).

Worked Examples

Worked Example

Conditional probability from contingency table

Problem

P(\text{passed}|\text{boy})

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge2 marks

State the condition for events

A

and

B

to be independent.

L1 · Knowledge2 marks

P(A)=0.4

P(B)=0.5

P(A\cap B)=0.2

. Are

A

and

B

independent?

L2 · Routine Procedures2 marks

P(B)=0.3

P(A\cap B)=0.12

. Find

P(A|B)

L2 · Routine Procedures3 marks

A bag has 3 red and 5 blue balls. Two are drawn without replacement. Find

P(\text{both red})

L3 · Complex Procedures4 marks

P(A)=0.6

P(B)=0.5

P(A\cup B)=0.8

. Find

P(A|B)

L3 · Complex Procedures6 marks

A disease has 2% prevalence. Test is 95% sensitive (P(+|disease)=0.95) and 90% specific (P(−|no disease)=0.90). Find P(disease|positive test).

L4 · Problem Solving4 marks

Three fair coins are tossed. Given at least one head occurred, find the probability of all three heads.

L4 · Problem Solving5 marks

Events

A

and

B

are independent.

P(A)=p

and

P(B)=p

. Find the range of

p

for

P(A\cup B)<0.75

Statistics

Measurement