How do mutually exclusive and independent differ?

Mutually exclusive events cannot both happen, so add; independent events do not affect each other, so multiply.

Which totals are prime?

Totals run from 2 to 12 and the primes among them are 2, 3, 5, 7 and 11.

Why add two terms for same colour?

Same colour means two red or two white, which are exclusive, so their counts are added.

S6 Mathematics: Probability Practice Paper 3

2026-11-03

Tutor Prep Guide · Secondary Mathematics

Set three opens with single events on a die, a multiple of four, a heart and a two-colour bag, then two tails, a dice total of seven and same-colour draws, then at least two heads and prime totals, ending with the error of multiplying mutually exclusive events as if independent.

Quick answer　1/3, 1/6, 1/4, 3/8, 1/4, 1/6, 13/28, 1/2, 5/12 and 0.9.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 Mathematics: Probability – Tutor Lesson Plan
Level	S6

02　Questions (10 items)

FoundationA fair die is rolled once. What is the probability of a score below 3?
FoundationA fair die is rolled once. What is the probability of a multiple of 4?
FoundationOne card is drawn from a 52-card deck. What is the probability it is a heart?
FoundationA bag holds 5 red and 3 blue balls. One ball is drawn at random. What is the probability it is blue?
IntermediateTwo fair coins are tossed. What is the probability that both show tails?
IntermediateTwo fair dice are rolled. What is the probability that the total is 7?
IntermediateA bag holds 5 red and 3 white balls. Two balls are drawn without replacement. What is the probability they are the same colour?
ChallengeThree fair coins are tossed. What is the probability of at least two heads?
ChallengeTwo fair dice are rolled. What is the probability that the total is a prime number?
Error redoGiven A and B are mutually exclusive with P(A) = 0.4 and P(B) = 0.5, find P(A or B).

03　Answers and one-line notes

#	Answer	One-line note
1	1/3	Only 1 and 2 qualify, so 2 out of 6 is one third.
2	1/6	Only 4 of the six outcomes qualifies, so the probability is 1/6.
3	1/4	There are 13 hearts, so 13 over 52 is one quarter.
4	3/8	Three of the eight balls are blue, so the probability is 3/8.
5	1/4	Only TT of the four outcomes matches, so the probability is one quarter.
6	1/6	Six of the 36 pairs give a total of 7, so 6 over 36 is one sixth.
7	13/28	Add C(5,2) and C(3,2) over C(8,2), that is 13 over 28.
8	1/2	Three outcomes have exactly two heads and one has three, so 4 out of 8 is one half.
9	5/12	The prime totals 2, 3, 5, 7 and 11 come from 1 + 2 + 4 + 6 + 2 pairs, so 15 over 36 is 5/12.
10	0.9	Mutually exclusive events cannot both happen, so add to get 0.9; multiplying to 0.2 wrongly assumes independence.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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