Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Relative frequency

Estimating probability from experiments.

9 original questions, 29 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Ravi flips a coin 50 times. It lands on heads 28 times.

Work out the relative frequency of heads. Give your answer as a decimal.

2 marks
Show answer
0.56
2

A spinner has four colours. This table shows the relative frequency of each colour from an experiment.

ColourRedBlueGreenYellow
Relative frequency0.30.25x0.15
  1. Work out the value of x.
  2. The spinner is spun 80 more times. Estimate how many times it lands on blue.
3 marks
Show answer
a) 0.3 b) 20
3

Amy and Ben each spin the same spinner and record how many times it lands on red.

Number of spinsNumber of reds
Amy5018
Ben15042

Using all of the results, work out the best estimate for the probability that the spinner lands on red.

2 marks
Show answer
310
4

Chloe takes a counter from a bag, records its colour and puts it back. She does this 80 times.

ColourRedYellowBlue
Frequency203624
  1. Write down the best estimate of the probability that the next counter is yellow.
  2. There are 40 counters in the bag. Estimate how many are yellow.
3 marks
Show answer
a) 9/20 b) 18
5

A three-colour spinner can land on red, white or blue.

The spinner is spun 100 times. The table shows the results.

Colourredwhiteblue
Frequency253540
  1. Work out the best estimate for the probability that the spinner lands on blue.
  2. Two of these identical spinners are spun together. Use the results to estimate the probability that both spinners land on red.

Assume the two spinners operate independently.

5 marks
Show answer
a) 2/5 (or 0.4) b) 1/16 (or 0.0625)
6

A spinner has three colours. It is spun 50 times.

ColourRedBlueGreen
Frequency181220
  1. Work out the relative frequency of green.
  2. Estimate how many times the spinner lands on green in 200 spins.
3 marks
Show answer
a) 0.4 b) 80
7

Tom rolls a dice several times and records the number of sixes.

Number of rolls1050100500
Number of sixes3112085
Relative frequency0.30.2
  1. Complete the table.
  2. Which of the four results gives the most reliable estimate of the probability of rolling a six? Give a reason.
  3. Is the dice fair? Use the table to explain your answer.
4 marks
Show answer
a) 0.22 and 0.17 b) 500 rolls, because it has the most trials c) Probably fair: 0.17 is very close to 1/6 (0.167)
8

Layla drops a drawing pin 20 times and it lands point up 13 times. Ben drops the same drawing pin 200 times and it lands point up 96 times.

  1. Whose results give the better estimate of the probability of landing point up? Give a reason.
  2. Use the better estimate to predict how many times the pin lands point up in 1000 drops.
3 marks
Show answer
a) Ben, because he did more trials b) 480
9

A gardener finds that the relative frequency of a seed growing into a plant is 0.85.

  1. She plants 240 seeds. Estimate how many grow into plants.
  2. She wants at least 400 plants. Estimate the smallest number of seeds she should plant.
4 marks
Show answer
a) 204 b) 471

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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