Grade 11 Probability — How to Identify the Question Type

Grade 11 Probability questions usually give you a diagram or table and ask you to read or calculate from it — but the same numbers can be asked about in different ways. Before calculating anything, work out whether the events are mutually exclusive, complementary, or independent, since each relationship uses a different rule.

Type 1: Venn diagrams

Trigger words: "Draw a Venn diagram", "represented on the Venn diagram", overlapping circles already given

Trigger structure: Two (or three) events shown as overlapping circles inside a rectangle representing the sample space.

Method (no numbers — just the steps)

Fill in the intersection (the overlap) first, using any given P(A and B)
Fill in the remaining part of each circle by subtracting the intersection from each event's total
Fill in the region outside both circles by subtracting everything already placed from the total
Read off whatever probability the question asks for as (favourable region) / (total)

Grade 11Paper 1Level 2 — Routine Procedures

In a class of 40 learners, 18 take Geography (G), 15 take History (H), and 6 take both. Draw a Venn diagram to represent this information, and calculate the probability that a learner chosen at random takes NEITHER subject.

Practice question — not sourced from a past paper.

Common mistake

Filling in each circle's full given probability without first subtracting the overlap, which double-counts the intersection.

See the progression — same type, increasing difficulty

Easy

Of 50 people surveyed, 30 like tea, 25 like coffee, and 12 like both. Calculate the probability that a person chosen at random likes tea OR coffee.

Practice question — not sourced from a past paper.

Medium

In a survey of 60 learners, 22 play soccer (S), 20 play netball (N), and 25 play neither sport. Calculate the number of learners who play BOTH soccer and netball.

Practice question — not sourced from a past paper.

Hard

A Venn diagram shows three events, A, B and C, with various overlaps. P(A) = 0,4, P(B) = 0,35, P(C) = 0,3, P(A and B) = 0,1, P(B and C) = 0,08, P(A and C) = 0,12, and P(A and B and C) = 0,03. Calculate P(A or B or C).

Practice question — not sourced from a past paper.

Type 2: Mutually exclusive and complementary events

Trigger words: "Mutually exclusive", "complementary events", "P(not A)"

Trigger structure: Mutually exclusive: two events that cannot happen at the same time (P(A and B) = 0). Complementary: two mutually exclusive events that together cover every possible outcome (P(A) + P(not A) = 1).

Do not confuse with: Independent events (Type 3) — mutually exclusive is about whether two events can occur TOGETHER; independent is about whether one event AFFECTS the other's probability. They are different ideas, and an event generally cannot be both mutually exclusive and independent of another (unless one has probability 0).

Method (no numbers — just the steps)

Decide whether the events given can occur together — if not, they're mutually exclusive
If mutually exclusive, use P(A or B) = P(A) + P(B), with no subtraction needed
For a complement, use P(not A) = 1 − P(A)

Grade 11Paper 1Level 1 — Knowledge

A bag contains coloured balls. The probability of drawing a red ball is 0,3 and the probability of drawing a blue ball is 0,25. No ball is both red and blue. Calculate the probability of drawing a ball that is red OR blue.

Practice question — not sourced from a past paper.

Common mistake

Subtracting P(A and B) when the events are mutually exclusive — since P(A and B) = 0 by definition, the standard formula still works, but many students subtract a non-zero estimate by mistake.

See the progression — same type, increasing difficulty

Easy

The probability that it rains tomorrow is 0,2. Calculate the probability that it does NOT rain tomorrow.

Practice question — not sourced from a past paper.

Medium

Events A and B are mutually exclusive, with P(A) = 0,45 and P(A or B) = 0,7. Calculate P(B).

Practice question — not sourced from a past paper.

Hard

In a group of 80 learners, every learner studies Mathematics, Physical Sciences, or both. 50 study Mathematics and 45 study Physical Sciences. Determine whether the events 'studies Mathematics' and 'studies Physical Sciences' are mutually exclusive, with reasons.

Practice question — not sourced from a past paper.

Type 3: Independent events

Trigger words: "Independent events", "Show that A and B are independent", "with replacement"

Trigger structure: Two events where the outcome of one does not affect the probability of the other — test this using P(A and B) = P(A) × P(B).

Do not confuse with: Dependent events (Type 4) — if the events happen 'without replacement' or one outcome changes the conditions for the next, they are dependent, not independent.

Method (no numbers — just the steps)

Calculate P(A), P(B), and the given or calculated P(A and B)
Check whether P(A and B) = P(A) × P(B)
If the values match, state the events are independent; if not, state they are dependent

Grade 11Paper 1Level 2 — Routine Procedures

P(A) = 0,4, P(B) = 0,5, and P(A and B) = 0,2. Determine whether events A and B are independent.

Practice question — not sourced from a past paper.

Common mistake

Assuming events are independent just because the question doesn't explicitly say 'dependent' — independence must be tested with the multiplication rule, not assumed.

See the progression — same type, increasing difficulty

Easy

A fair coin is tossed and a fair die is rolled. Calculate the probability of getting heads on the coin AND a 6 on the die.

Practice question — not sourced from a past paper.

Medium

P(A) = 0,3 and P(B) = 0,6. Events A and B are independent. Calculate P(A and B).

Practice question — not sourced from a past paper.

Hard

P(A) = 0,5, P(B) = x, and P(A and B) = 0,15. Events A and B are independent. Calculate the value of x.

Practice question — not sourced from a past paper.

Type 4: Tree diagrams and contingency tables for dependent events

Trigger words: "Without replacement", "Draw a tree diagram", a two-way table of results is given

Trigger structure: The probability of the second event changes because of what happened in the first — usually signalled by 'without replacement' or a sequence of dependent draws.

Do not confuse with: Independent events (Type 3) — 'without replacement' is the clearest signal that the second probability depends on the first outcome.

Method (no numbers — just the steps)

Draw the tree diagram, branching for each possible outcome at each stage
Label each branch with its probability, adjusting later branches for what already happened
Multiply along a path to find the probability of that specific sequence of outcomes
Add the probabilities of separate paths that all satisfy the question's condition

Grade 11Paper 1Level 3 — Complex Procedures

A bag contains 5 red and 3 blue balls. Two balls are drawn one after the other, WITHOUT replacement. Calculate the probability that both balls are red.

Practice question — not sourced from a past paper.

Common mistake

Using the same probability for the second draw as the first, forgetting that removing an item without replacement changes the total and the count remaining.

See the progression — same type, increasing difficulty

Easy

A bag contains 4 yellow and 6 green sweets. One sweet is drawn and eaten, then a second sweet is drawn. Calculate the probability that the first sweet is yellow and the second is green.

Practice question — not sourced from a past paper.

Medium

A box contains 3 defective and 7 working light bulbs. Two bulbs are selected one after the other, without replacement. Calculate the probability that AT LEAST ONE of the two bulbs is defective.

Practice question — not sourced from a past paper.

Hard

A survey of 200 people recorded whether they own a car and whether they own a bicycle: Owns car: 80 own a bicycle, 50 don't. Does not own a car: 30 own a bicycle, 40 don't. If a person is chosen at random, calculate the probability that they own a bicycle, GIVEN that they own a car.

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.