What are the numerator and denominator?

The denominator counts all equally likely outcomes and the numerator counts the favourable ones.

How does drawing without replacement change things?

The denominator of the second draw drops by one because a ball has gone.

Can P(A or B) always be added directly?

Only for mutually exclusive events, otherwise subtract P(A and B).

S6 Mathematics: Probability Practice Paper 1

2026-11-03

Tutor Prep Guide · Secondary Mathematics

Set one starts with single events on dice, cards and balls, then two coins, two dice totals and draws without replacement, then three coins and a large total, ending with the addition rule error of forgetting the overlap.

Quick answer　1/6, 1/2, 1/4, 3/5, 1/2, 1/6, 5/14, 3/8, 1/6 and 0.7.

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 getting 4?
FoundationA fair die is rolled once. What is the probability of an even number?
FoundationOne card is drawn from a 52-card deck. What is the probability it is a heart?
FoundationA bag holds 3 red and 2 blue balls. One ball is drawn at random. What is the probability it is red?
IntermediateTwo fair coins are tossed. What is the probability that both show the same face?
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 both are red?
ChallengeThree fair coins are tossed. What is the probability of exactly two heads?
ChallengeTwo fair dice are rolled. What is the probability that the total is at least 10?
Error redoGiven P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2, find P(A or B).

03　Answers and one-line notes

#	Answer	One-line note
1	1/6	Only one of the six equally likely outcomes is 4.
2	1/2	The even results 2, 4 and 6 number three, so 3 out of 6 is one half.
3	1/4	There are 13 hearts, so 13 over 52 is one quarter.
4	3/5	Three of the five balls are red, so the probability is 3/5.
5	1/2	Two of the four outcomes, HH and TT, match, so 2 out of 4 is one half.
6	1/6	Of the 36 equally likely pairs, 6 give a total of 7, so the answer is 1/6.
7	5/14	Take C(5,2) over C(8,2), which is 10 over 28, that is 5/14.
8	3/8	Three of the eight outcomes give two heads, so the probability is 3/8.
9	1/6	The totals 10, 11 and 12 arise from 3 + 2 + 1 pairs, so 6 over 36 is 1/6.
10	0.7	Add the two probabilities and subtract the overlap: 0.5 + 0.4 – 0.2 = 0.7.

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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