[discia] GCSE Maths › Probability › Relative Frequency

Relative Frequency

discia.org 10 questions · 35 marks
Name Date
  1. Either paper 4 marks

    A spinner can land on white, black, orange or purple. The spinner is spun 100 times.

    The table gives the results.

    ColourWhiteBlackOrangePurple
    Frequency19361134
    (a)

    Calculate the relative frequency of white. Give your answer as a decimal.

    (b)

    The spinner is spun 200 more times. Estimate the number of times it will land on white.

    Show answer
    (a) \(0.19\)
    (b) \(38\)
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  2. Either paper 4 marks

    A drawing pin is dropped onto a table many times.

    Out of \(50\) drops, it lands point up \(14\) times.

    (a)

    Calculate the relative frequency that it lands point up.

    Give your answer as a fraction in its simplest form.

    (b)

    Calculate the relative frequency as a percentage.

    Show answer
    (a) \(\frac{7}{25}\)
    (b) \(28\%\)
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  3. Either paper 3 marks

    Amara wants to test whether a coin is fair. She flips the coin 200 times.

    It lands on heads 80 times.

    (a)

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

    (b)

    Do you think the coin is fair? Give a reason for your answer.

    Show answer
    (a) \(0.4\)
    (b) No — the relative frequency of 0.4 is a long way from 0.5, so the coin looks biased.
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  4. Either paper 3 marks

    A bag of counters was tested 340 times.

    The relative frequency of green was \(0.35\).

    (a)

    Work out how many times the counter taken was green.

    (b)

    Work out how many times it was something else.

    Show answer
    (a) \(119\)
    (b) \(221\)
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  5. Either paper 4 marks
    A spinner has sections coloured gold, silver, bronze and grey. It was spun 100 times. The table shows the relative frequency of each colour.
    ColourRelative frequency
    gold0.15
    silver0.35
    bronze0.2
    grey
    (a)

    Work out the relative frequency of grey.

    (b)

    Calculate how many times the spinner landed on grey.

    Show answer
    (a) \(0.3\)
    (b) \(30\)
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  6. Either paper 3 marks
    Zara and Jack each spin the same biased coin a number of times. The table shows information about the results.
    JackZara
    Number of spins275175
    Relative frequency of heads0.160.28
    (a)

    How many more heads did Zara spin than Jack?

    (b)

    Zara says, "My estimate of the probability of the coin landing on heads must be the best, because 0.28 is greater than 0.16."

    Is she correct?

    Tick a box. Yes / No

    Give a reason for your answer.

    Show answer
    (a) \(5\)
    (b) No. Jack spun the coin more times (275 against 175), so Jack's estimate is the better one. A larger relative frequency does not make an estimate better.
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  7. Either paper 4 marks
    500 seeds were planted in a greenhouse. The number of seeds that germinated was recorded after every 100 seeds. The table shows some information about the results.
    Total number of seeds100200300400500
    Total number of seeds that germinated732486465
    Relative frequency of seeds that germinated0.070.16
    The graph shows the two relative frequencies that are already in the table. 1002003004005000.050.10.150.20.250.30.350.40Total number of seedsRelative frequency of seeds that germinated
    (a)

    Complete the table. Give each relative frequency as a decimal.

    (b)

    Write down the best estimate of the probability that a seed planted in the greenhouse germinates.

    Show answer
    (a) \(0.16,\ 0.16,\ 0.13\)
    (b) \(0.13\)
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  8. Either paper 4 marks

    Isaac and Nadia are testing the same spinner. They each want to estimate the probability that it lands on red.

    Isaac spins it 60 times. It lands on red 30 times.

    Nadia spins it 40 times. It lands on red 28 times.

    (a)

    Whose results give the more reliable estimate of the probability? Give a reason for your answer.

    (b)

    They put all of their results together. Use all 100 spins to work out the best estimate of the probability that the spinner lands on red.

    Show answer
    (a) Isaac — Isaac did 60 spins and Nadia did only 40, and the more trials there are the closer the relative frequency is likely to be to the true probability.
    (b) \(0.58\)
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  9. Either paper 3 marks

    A biased dice is rolled a number of times.

    It landed on blue \(24\) times.

    The relative frequency of landing on blue is \(0.3\).

    (a)

    Work out how many rolls there were altogether.

    (b)

    Calculate the relative frequency of not landing on blue.

    Show answer
    (a) \(80\ \text{rolls}\)
    (b) \(0.7\)
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  10. Either paper 3 marks

    A packing plant checks 700 eggs. Of these, 84 are cracked.

    The line is stopped if more than 4% of the eggs are cracked.

    Does the line have to be stopped?

    You must show your working.

    Show answer
    Yes — the relative frequency is \(0.12\), which is 12%, and that is more than 4%.
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discia.org Relative Frequency · sheet 1
Answers Relative Frequency · sheet 1
  1. (a) \(0.19\)
    (b) \(38\)
  2. (a) \(\frac{7}{25}\)
    (b) \(28\%\)
  3. (a) \(0.4\)
    (b) No — the relative frequency of 0.4 is a long way from 0.5, so the coin looks biased.
  4. (a) \(119\)
    (b) \(221\)
  5. (a) \(0.3\)
    (b) \(30\)
  6. (a) \(5\)
    (b) No. Jack spun the coin more times (275 against 175), so Jack's estimate is the better one. A larger relative frequency does not make an estimate better.
  7. (a) \(0.16,\ 0.16,\ 0.13\)
    (b) \(0.13\)
  8. (a) Isaac — Isaac did 60 spins and Nadia did only 40, and the more trials there are the closer the relative frequency is likely to be to the true probability.
    (b) \(0.58\)
  9. (a) \(80\ \text{rolls}\)
    (b) \(0.7\)
  10. Yes — the relative frequency is \(0.12\), which is 12%, and that is more than 4%.
discia.org Relative Frequency · sheet 1