Printable · GCSE Foundation · ages 14-16

Relative frequency and the probability scale worksheet — GCSE Foundation

Fifteen questions on "relative frequency and the probability scale" — DfE statement P3. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Relative frequency and the probability scale worksheet — GCSE Foundation

Maths · GCSE Foundation · P3 · Relative frequency and the probability scale · 15 questions

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1.Two goalkeepers face penalty kicks. Elin saves 34% of the penalties she faces. Noah saves 11/32 of the penalties he faces. Which statement correctly compares them?
(a)Elin — 34 is bigger than 11.
(b)Noah — 32 is a bigger denominator.
(c)Noah — 11/32 = 0.34375, above 34%.
(d)Equal — both round to 34% to the nearest percent.
2.The probability that a pupil chosen at random has a nut allergy is 1/10. There are 30 pupils in a class. Work out how many of the 30 pupils would be expected to have a nut allergy.
(a)1 pupil
(b)3 pupils
(c)27 pupils
(d)10 pupils
3.A spinner is spun 50 times. It lands on green 18 times. Work out the relative frequency of landing on green.
(a)0.36
(b)0.18
(c)0.64
(d)0.036
4.A fair six-sided dice is rolled once. Work out the probability that the score is an odd number. Give your answer as a decimal.
(a)0.3
(b)0.33
(c)0.5
(d)0.17
5.Two games at a school fete are played independently. The probability of winning game X is 3/8. The probability of winning game Y is 0.4. Which statement correctly compares the two games?
(a)Game X — 3/8 has the larger denominator.
(b)Equal — 3/8 rounds to 0.4 to one decimal place.
(c)Game Y — 0.4 is greater than 3/8.
(d)Game X — 3 is greater than 0, the units digit of 0.4.
6.An ordinary six-sided dice, numbered 1 to 6, is rolled 30 times and lands on a 6 seven times. Ravi says the theoretical probability of rolling a 6 and the relative frequency of rolling a 6 in this trial are the same number. Is Ravi right?
(a)Yes — relative frequency always equals theory.
(b)Yes — the theoretical probability has now become 7/30.
(c)No — 7/30 is the relative frequency; theory stays 1/6.
(d)Neither can be found — 30 rolls is too few to tell.
7.In a trial, a drawing pin was dropped 80 times and landed point-up 52 times. Assuming this relative frequency continues, work out how many times you would expect it to land point-up in 300 drops.
(a)195
(b)105
(c)156
(d)52
8.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.
(a)4 times as likely
(b)3 times as likely
(c)12 times as likely
(d)6 times as likely
9.A bag is known to contain red, blue and green counters in equal numbers, so the theoretical probability of taking each colour is 1/3. In 90 trials with replacement, red was taken 38 times, blue was taken 26 times and green was taken 26 times. Which colour is over-represented compared with its theoretical probability?
(a)Green
(b)Blue
(c)Red
(d)None of the three colours
10.On the probability scale from 0 to 1, which word best describes an event with probability 0.9?
(a)unlikely
(b)likely
(c)certain
(d)evens
11.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.
(a)1/6
(b)1/5
(c)5/6
(d)1/2
12.A quality inspector tests 145 light bulbs and finds that 33 are faulty. Work out the relative frequency of a bulb being faulty, as a percentage correct to 1 decimal place.
(a)77.2%
(b)22.8%
(c)33.0%
(d)22.7%
13.The probability that a spinner lands on blue is 2/5. Write this probability as a percentage.
(a)20%
(b)40%
(c)2%
(d)4%
14.An ordinary pack of 52 playing cards contains 13 hearts. One card is taken at random from the pack. Work out the probability that the card is not a heart. Give your answer as a percentage.
(a)39%
(b)50%
(c)25%
(d)75%
15.The probability that Amelia's bus is late on a school morning is 9/10. Write this probability as a percentage.
(a)90%
(b)9%
(c)10%
(d)0.9%

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