From Real Exams Quiz

O Level Additional Mathematics Statistics Probability Quiz

Free O Level A Maths Statistics quiz, HY3 Exam version, with questions, answers, and O Level-style practice for Singapore students.

These static practice materials are generated from the site's syllabus and paper-generation workflow, with source and model context shown so students and parents can evaluate the material before use.

O Level Additional Mathematics From Real Exams Generated by Tencent HY3 Free Updated 2026-08-17

Back to Subject Browse Free Exam Papers

Questions

O-Level Additional Mathematics Quiz - Statistics Probability

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 60 minutes
Total Marks: 40

Instructions:

Answer all 20 questions.
Show your working clearly where required.
Section A: 10 short questions (2 marks each). Section B: 6 structured questions (3 marks each). Section C: 4 extended questions (4 marks each).
Use calculators where appropriate. Give answers correct to 3 significant figures where not exact.

Section A (Questions 1–10, 2 marks each)

1. A bag contains 5 red and 7 blue marbles. A marble is drawn at random. Find the probability that it is red.

2. Two fair dice are rolled. Find the probability that the sum of the scores is 7.

3. Events A and B are such that $P(A) = 0.4$ , $P(B) = 0.5$ , and $P(A \cap B) = 0.2$ . Find $P(A \cup B)$ .

4. A coin is tossed 3 times. Find the probability of getting exactly 2 heads.

5. The table shows the number of students in a class by gender and favourite subject.

	Math	Science	Total
Male	8	6	14
Female	10	7	17
Total	18	13	31

A student is chosen at random. Find the probability the student is female given they like Math.

6. A box has 4 green, 3 yellow, and 5 red pens. Two pens are drawn without replacement. Find the probability both are red.

7. For a binomial distribution $X \sim B(10, 0.3)$ , state the mean of $X$ .

8. Events A and B are independent with $P(A)=0.6$ and $P(B)=0.4$ . Find $P(A \cap B)$ .

9. A spinner has 4 equal sectors labelled 1, 2, 3, 4. Find the probability of spinning an even number.

10. From a deck of 52 cards, one card is drawn. Find the probability it is a heart.

Section B (Questions 11–16, 3 marks each)

11. A survey of 80 students found 50 like basketball, 30 like badminton, and 10 like both. Find the probability a randomly selected student likes basketball or badminton.

12. A bag contains 3 white and 2 black balls. Two balls are drawn at random without replacement. Find the probability that exactly one is white.

13. A random variable $X \sim B(n, p)$ has mean 6 and variance 2.4. Find $n$ and $p$ .

14. The probability that a machine produces a defective item is 0.1. In a batch of 5 items, find the probability exactly 2 are defective. Use $X \sim B(5, 0.1)$ .

15. Events A and B are such that $P(A)=0.5$ , $P(B)=0.3$ , $P(A|B)=0.6$ . Find $P(A \cap B)$ and determine if A and B are independent.

16. The table shows the probability distribution of a discrete random variable $X$ .

$x$	1	2	3	4
$P(X=x)$	0.2	$k$	0.3	0.1

Find $k$ and $E(X)$ .

Section C (Questions 17–20, 4 marks each)

17. A box contains 5 red, 3 blue, and 2 green balls. Three balls are drawn without replacement. Find the probability that they are all of different colours.

18. In a class of 20 students, 12 take Additional Mathematics and 8 take Physics. 5 take both. A student is chosen at random. Find the probability the student takes Additional Mathematics given they take Physics. Hence find the probability the student takes neither.

19. A biased coin has $P(\text{head})=0.6$ . The coin is tossed 4 times. Let $X$ be the number of heads.
(a) State the distribution of $X$ .
(b) Find $P(X \ge 3)$ .

20. The discrete random variable $X$ has probability distribution:

$x$	0	1	2	3
$P(X=x)$	0.1	0.2	$p$	0.3

(a) Find $p$ .
(b) Find $E(X)$ and $Var(X)$ .

Free quiz and exam paper access

Enter your details to view this paper

Your access is remembered on this device.

Answers

O-Level Additional Mathematics Quiz - Statistics Probability (Answer Key)

Total Marks: 40
Topic: Statistics Probability

Section A Answers (Q1–10, 2 marks each)

Q1. Probability = $\frac{5}{5+7} = \frac{5}{12}$ .
Teaching note: Total marbles = 12, favourable = 5 red. $P(\text{red}) = \frac{\text{favourable}}{\text{total}}$ .
Marks: 1 for total, 1 for final answer.

Q2. Favourable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes. Total = 36. $P = \frac{6}{36} = \frac{1}{6}$ .
Teaching note: Sum 7 has 6 combinations out of 6×6=36 equally likely outcomes.
Marks: 1 for favourable count, 1 for answer.

Q3. $P(A \cup B) = P(A)+P(B)-P(A\cap B) = 0.4+0.5-0.2 = 0.7$ .
Teaching note: Addition rule for union.
Marks: 1 for formula, 1 for answer.

Q4. $X \sim B(3,0.5)$ , $P(X=2) = \binom{3}{2}(0.5)^2(0.5)^1 = 3 \times 0.125 = 0.375$ .
Teaching note: Exactly 2 heads from 3 tosses.
Marks: 1 for setup, 1 for answer.

Q5. $P(\text{Female}|\text{Math}) = \frac{10}{18} = \frac{5}{9}$ .
Teaching note: Conditional: among Math lovers (18), females = 10.
Marks: 1 for denominator, 1 for answer.

Q6. $P(\text{both red}) = \frac{5}{12} \times \frac{4}{11} = \frac{20}{132} = \frac{5}{33}$ .
Teaching note: Without replacement: second draw has 4 red of 11 left.
Marks: 1 for method, 1 for answer.

Q7. Mean = $np = 10 \times 0.3 = 3$ .
Teaching note: Binomial mean formula.
Marks: 2 for correct statement.

Q8. Independent → $P(A\cap B)=P(A)P(B)=0.6\times0.4=0.24$ .
Teaching note: Independence definition.
Marks: 2 for answer.

Q9. Even sectors: 2,4 → 2 of 4. $P = \frac{2}{4}=0.5$ .
Marks: 2.

Q10. Hearts = 13 of 52. $P = \frac{13}{52}=\frac{1}{4}$ .
Marks: 2.

Section B Answers (Q11–16, 3 marks each)

Q11. $P(B \cup M) = \frac{50+30-10}{80} = \frac{70}{80} = \frac{7}{8}$ .
Teaching note: Inclusion-exclusion on 80 students.
Marks: 1 count, 1 subtraction, 1 answer.

Q12. Exactly one white: (W,B) or (B,W).
$P = \frac{3}{5}\times\frac{2}{4} + \frac{2}{5}\times\frac{3}{4} = \frac{6}{20}+\frac{6}{20}=\frac{12}{20}=0.6$ .
Marks: 1 for cases, 1 for calc, 1 answer.

Q13. Mean $np=6$ , Var $np(1-p)=2.4$ . So $6(1-p)=2.4 \Rightarrow 1-p=0.4 \Rightarrow p=0.6$ . Then $n=10$ .
Marks: 1 eqn, 1 p, 1 n.

Q14. $P(X=2)=\binom{5}{2}(0.1)^2(0.9)^3 = 10 \times 0.01 \times 0.729 = 0.0729$ .
Marks: 1 formula, 1 sub, 1 answer.

Q15. $P(A\cap B)=P(A|B)P(B)=0.6\times0.3=0.18$ . Independent if $P(A\cap B)=P(A)P(B)=0.15$ ; since 0.18≠0.15, NOT independent.
Marks: 1 calc, 1 compare, 1 conclusion.

Q16. $\sum P =1 \Rightarrow 0.2+k+0.3+0.1=1 \Rightarrow k=0.4$ .
$E(X)=1(0.2)+2(0.4)+3(0.3)+4(0.1)=0.2+0.8+0.9+0.4=2.3$ .
Marks: 1 k, 1 E setup, 1 answer.

Section C Answers (Q17–20, 4 marks each)

Q17. Total ways = $\binom{10}{3}=120$ . Favourable: 1 red,1 blue,1 green = $5\times3\times2=30$ . $P=\frac{30}{120}=0.25$ .
Marks: 1 total, 1 favourable, 1 division, 1 answer.

Q18. $P(AM|P)=\frac{5}{8}=0.625$ . Neither = 20-(12+8-5)=5, so $P=\frac{5}{20}=0.25$ .
Marks: 1 cond, 1 neither count, 1 each prob.

Q19. (a) $X \sim B(4,0.6)$ . (b) $P(X\ge3)=P(X=3)+P(X=4)=\binom{4}{3}(0.6)^3(0.4)+\binom{4}{4}(0.6)^4 = 4\times0.216\times0.4 + 0.1296 = 0.3456+0.1296=0.4752$ .
Marks: 1 dist, 1 setup, 1 calc, 1 answer.

Q20. (a) $0.1+0.2+p+0.3=1 \Rightarrow p=0.4$ . (b) $E=0(0.1)+1(0.2)+2(0.4)+3(0.3)=0+0.2+0.8+0.9=1.9$ . $E(X^2)=0+0.2+4(0.4)+9(0.3)=0.2+1.6+2.7=4.5$ . $Var=4.5-(1.9)^2=4.5-3.61=0.89$ .
Marks: 1 p, 1 E, 1 E(X²), 1 Var.