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IGCSE · Practice questions · Relative and expected frequencies

Trials tell the story.

Six original Cambridge-style questions on relative frequency, fairness and bias, and expected frequency.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
The method

Estimate from trials, predict from probability.

01
Recall
[1 marks]

A coin is thrown 80 times and lands heads 32 times. Find the relative frequency of heads.

  • \(32 \div 80 = 0.4\) ✓
02
Recall
[1 marks]

Explain what is meant by a biased spinner.

  • The outcomes are not all equally likely: some sections come up more often than others. ✓
03
Calculation
[1 marks]

The probability that a light bulb is faulty is 0.04. A shop receives 2500 bulbs. How many would you expect to be faulty?

  • \(0.04 \times 2500 = 100\) ✓
04
Calculation
[3 marks]

A four-sided spinner is spun 160 times. The results are: 1 came up 35 times, 2 came up 42 times, 3 came up 38 times and 4 came up 45 times.

(a) Find the relative frequency of 4. (b) Estimate how many 4s there would be in 800 spins.

  • (a) \(45 \div 160 = 0.28125\) (0.281) ✓
  • (b) \(0.28125 \times 800 = 225\) ✓
05
Analysis
[3 marks]

Tom throws a dice 50 times and gets 9 sixes. Sara throws the same dice 250 times and gets 46 sixes.

(a) Whose results are more reliable? Give a reason. (b) Find the best estimate of the probability of a six. (c) Does the dice appear to be fair?

  • (a) Sara's, because she did more trials. ✓
  • (b) \(\dfrac{9 + 46}{50 + 250} = \dfrac{55}{300} = 0.183\) (3 s.f.) ✓
  • (c) A fair dice gives \(\tfrac{1}{6} = 0.167\); 0.183 is close, so the dice appears fair. ✓
06
Analysis
[3 marks]

A random sample of 120 students at a school is asked how they travel to school. 42 of them walk.

The school has 1400 students. Estimate how many of them walk to school, and state one reason why this is only an estimate.

  • Relative frequency \(= 42 \div 120 = 0.35\). ✓
  • Estimate \(= 0.35 \times 1400 = 490\) students. ✓
  • It is only an estimate because a different sample of 120 could give a different number. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.