What is the fastest way for at least one?

Use the complement: subtract the probability of none from 1, which usually needs only one case counted.

How many pairs give a total above four?

Count all 36 pairs first, then the pairs with totals 2 to 4, and subtract.

Why does the denominator change on a second draw?

Without replacement the ball count drops, so the second denominator falls by one.

S6 Mathematics: Probability Practice Paper 2

2026-11-03

Tutor Prep Guide · Secondary Mathematics

Set two opens with single events on a die, primes, an ace and a two-colour bag, then two coins with exactly one head, a dice total of nine and draws without replacement, then the complement with three coins and a small total, ending with the addition rule error of forgetting the overlap.

Quick answer　1/3, 1/2, 1/13, 2/5, 1/2, 1/9, 1/3, 7/8, 5/18 and 0.8.

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 above 4?
FoundationA fair die is rolled once. What is the probability of a prime score?
FoundationOne card is drawn from a 52-card deck. What is the probability it is an ace?
FoundationA bag holds 4 red and 6 blue balls. One ball is drawn at random. What is the probability it is red?
IntermediateTwo fair coins are tossed. What is the probability of exactly one head?
IntermediateTwo fair dice are rolled. What is the probability that the total is 9?
IntermediateA bag holds 6 red and 4 white balls. Two balls are drawn without replacement. What is the probability both are red?
ChallengeThree fair coins are tossed. What is the probability of at least one head?
ChallengeTwo fair dice are rolled. What is the probability that the total is at most 5?
Error redoGiven P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.3, find P(A or B).

03　Answers and one-line notes

#	Answer	One-line note
1	1/3	Only 5 and 6 qualify, so 2 out of 6 is one third.
2	1/2	The primes 2, 3 and 5 number three, so 3 out of 6 is one half.
3	1/13	There are four aces, so 4 over 52 is one thirteenth.
4	2/5	Four of the ten balls are red, so the probability is 2/5.
5	1/2	Two of the four outcomes, HT and TH, match, so 2 out of 4 is one half.
6	1/9	Four of the 36 pairs give a total of 9, so 4 over 36 is one ninth.
7	1/3	Take C(6,2) over C(10,2), which is 15 over 45, that is 1/3.
8	7/8	Only one outcome has no head, so subtract 1/8 from 1 to get 7/8.
9	5/18	The totals 2 to 5 arise from 1 + 2 + 3 + 4 pairs, so 10 over 36 is 5/18.
10	0.8	Work out 0.6 + 0.5 – 0.3, giving 0.8, since the overlap counts once only.

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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