Relative & expected frequency: IGCSE Mathematics questions with answers
Free Relative & expected frequency questions for IGCSE Mathematics (0580), part of Probability. Each question has the answer and the marking points an examiner would look for.
The spinner is spun 500 times. Find the expected number of times it lands on yellow.
[2]
(c)
The spinner is spun twice. Find the probability that it lands on red both times or on blue both times.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.25
0.15 + 0.1 + x + 2x = 1 M1 0.25 A1
2
(b)
250
500 × 0.5 M1 250 A1
2
(c)
0.0325
0.152 + 0.12M1 0.0325 A1
2
Question 2Structured · 6 marksA* challenge
A bag contains x red sweets and (x + 4) yellow sweets. Two sweets are taken at random without replacement. The probability that both sweets are red is 1091.
(a)
Show that 17x2 − 77x − 40 = 0.
[3]
(b)
Solve the equation to find the number of sweets in the bag.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
x2x + 4 × x − 12x + 3 = 1091 leads to 17x2 − 77x − 40 = 0
x2x + 4 × x − 12x + 3 = 1091M1 cross-multiplied and expanded correctly M1 17x2 − 77x − 40 = 0 with no errors A1
3
(b)
x = 5, so 14 sweets
factorise or use the formula M1 x = 5 (other root rejected) A1 14 A1
3
Question 3Structured · 3 marks
A drawing pin is dropped 80 times. It lands point up 20 times.
(a)
Find the relative frequency of landing point up.
[1]
(b)
The pin is dropped 600 more times. Estimate how many times it lands point up.
[1]
(c)
Explain how the estimate could be made more reliable.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
14
14B1
1
(b)
150
150 B1
1
(c)
more trials
increase the number of trials B1
1
Question 4Structured · 3 marks
The table shows the probabilities of a biased spinner landing on each colour.
Colour
Red
Blue
Green
Yellow
Probability
0.15
0.30
0.30
x
Table 4.1
(a)
Find x.
[2]
(b)
The spinner is spun 200 times. Find the expected number of times it lands on blue.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.25
1 − sum M1 0.25 A1
2
(b)
60
60 B1
1
Question 5Structured · 3 marks
A bag contains 4 red, 4 blue and 3 green counters. One counter is taken at random.
(a)
Find the probability that it is red.
[1]
(b)
Find the probability that it is not green.
[1]
(c)
Find the probability that it is yellow.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
411
411B1
1
(b)
811
811B1
1
(c)
0
0 B1
1
Question 6Structured · 12 marksA* challenge
Three fair six-sided dice are thrown. The three scores can sometimes be arranged in an order that makes an arithmetic sequence (a sequence with a constant difference, which may be zero), for example 5, 1, 3 → 1, 3, 5.
(a)
Find the probability that the three scores can be arranged to make an arithmetic sequence.
[4]
(b)
Find the probability that the scores, in the order the dice are numbered, already make an arithmetic sequence.
[3]
(c)
Given that the three scores can be arranged to make an arithmetic sequence, find the probability that the three scores are all different.
[2]
(d)
Five fair dice are thrown. Find the probability that the five scores can be arranged to make an arithmetic sequence.
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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in