IGCSE Math RevisionQuestion 1
A coin is thrown \(200\) times and lands on heads \(116\) times.
Work out the relative frequency of heads.
Show the worked answer
- \(\frac{116}{200} = 0.58\)
Answer: \(0.58\)
Cambridge IGCSE Maths (0580) · Topic 8: Probability · 8.2
Cambridge IGCSE Maths 0580 Relative and Expected Frequency Questions
Relative and Expected Frequency questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 9 questions
- 9 Core
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 8.2 Relative and expected frequencies Core
Relative frequency as an estimate of probability; Expected frequency.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Relative and Expected Frequency questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
The probability that a spinner lands on red is \(0.15\). The spinner is spun \(300\) times.
How many times would you expect it to land on red?
Show the worked answer
- Expected frequency \(= 300 \times 0.15 = 45\).
Answer: \(45\)
Question 3
A spinner numbered 1 to 4 is spun 100 times. It lands on 1 23 times, on 2 31 times, on 3 26 times and on 4 20 times.
(a) Write down the relative frequency of landing on 2.
(b) Estimate how many times it lands on 4 in 600 spins.
Show the answer and mark scheme
- B1 (a) 0.31
- B1 (b) 120
Answer: (a) \(0.31\) (b) \(120\)
Question 4
Leila rolls a dice \(60\) times and gets a six \(18\) times.
(a) Work out the relative frequency of a six.
(b) How many sixes would you expect from a fair dice in \(60\) rolls? Is Leila's dice likely to be fair?
Show the worked answer
- (a) \(\frac{18}{60} = 0.3\)
- (b) Fair: \(60 \times \frac{1}{6} = 10\). \(18\) is much more than \(10\), so the dice is probably biased towards six.
Answer: (a) \(0.3\) (b) \(10\); probably not fair (biased)
Question 5
A spinner is spun \(100\) times. The results are in the table.
(a) Find the relative frequency of blue.
(b) The spinner is spun \(500\) more times. Estimate how many of these land on blue.
| Colour | Red | Blue | Green |
|---|---|---|---|
| Frequency | 34 | 41 | 25 |
Show the worked answer
- (a) \(\frac{41}{100} = 0.41\)
- (b) \(500 \times 0.41 = 205\)
Answer: (a) \(0.41\) (b) \(205\)
Question 6
The probability that a bus is late on any day is \(0.08\).
How many times would you expect the bus to be late in \(250\) days?
Show the worked answer
- \(250 \times 0.08 = 20\)
Answer: \(20\)
Question 7
A biased dice is thrown 200 times. The relative frequency of a six is 0.3.
(a) How many sixes were thrown?
(b) How many sixes would you expect in 50 more throws?
Show the answer and mark scheme
- B1 (a) 60
- B1 (b) 15
Answer: (a) \(60\) (b) \(15\)
Question 8
In a survey of 80 cars passing a school, 20 were red.
(a) Estimate the probability that the next car is red.
(b) Estimate how many of the next 500 cars will be red.
Show the answer and mark scheme
- B1 (a) 0.25 oe
- B1 (b) 125
Answer: (a) \(0.25\) (b) \(125\)
Question 9
Two students test the same drawing pin. Ali drops it \(20\) times and it lands point up \(7\) times. Bea drops it \(200\) times and it lands point up \(54\) times.
Using all the results, find the best estimate of the probability that the pin lands point up.
Show the worked answer
- Combine the trials: \(7 + 54 = 61\) point up in \(20 + 200 = 220\) drops.
- Best estimate \(= \frac{61}{220}\) (about \(0.277\)); more trials give a more reliable estimate.
Answer: \(\frac{61}{220}\) (about \(0.277\))
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Probability practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Probability revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test relative and expected frequency?
Relative and Expected Frequency is on both tiers (syllabus 8.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more relative and expected frequency questions?
In the 0580 practice for topic 8 (Probability), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.