IGCSE Mathematics: Probability Practice Questions
The probability of an event is the number of favourable outcomes divided by the total number of possible outcomes. All the probabilities of an exhaustive set of outcomes add to 1.
Topic 8.1 of Cambridge IGCSE Mathematics 0580 rewards leaving answers as fractions and never converting to a rounded decimal partway through. Expected frequency questions are the ones most often misread. The questions below cover all four standard types.
What you need to know for Probability
- Probability of an eventFavourable outcomes divided by total outcomes. Always a value between 0 and 1 inclusive.
- ComplementThe probability that an event does not happen is 1 minus the probability that it does.
- Total probabilityFor a set of outcomes covering every possibility, the probabilities add to 1. Use this to find a missing probability.
- Relative frequencyThe number of times an outcome occurred divided by the number of trials. It estimates probability and improves as trials increase.
- Expected frequencyProbability multiplied by the number of trials. It gives the number of times an outcome is expected, not a guarantee.
- Fair or biasedCompare relative frequency with the theoretical probability. A large difference over many trials suggests bias.
IGCSE Mathematics Probability questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
A bag contains 5 red, 3 blue and 4 green counters. One counter is taken at random. Find the probability that it is red, and the probability that it is not red.
Show the worked answer
- Count the total number of counters: 5 + 3 + 4 = 12.
- There are 5 red counters, so P(red) = 5 over 12.
- For not red, either count the others (3 + 4 = 7) or use the complement.
- P(not red) = 1 minus 5 over 12 = 7 over 12. The two probabilities add to 1, as they must.
A die is rolled 200 times and a six appears 34 times. Calculate the relative frequency of rolling a six, and comment on whether the die appears to be fair.
Show the worked answer
- Relative frequency = number of successes divided by number of trials = 34 divided by 200.
- 34 divided by 200 = 0.17.
- For a fair die the theoretical probability of a six is 1 over 6, which is 0.167 to 3 decimal places.
- 0.17 is very close to 0.167, and 200 trials is a reasonably large sample, so there is no evidence of bias. The die appears fair.
Using the same bag of 5 red, 3 blue and 4 green counters, a counter is drawn and replaced 300 times. Calculate the expected number of green counters.
Show the worked answer
- P(green) = 4 over 12, which simplifies to 1 over 3.
- Expected frequency = probability x number of trials.
- Expected number = one third x 300.
- Expected number = 100 green counters. This is an expectation, not a guarantee, so the actual result will vary around it.
A spinner has three outcomes A, B and C. P(A) = 0.35 and P(B) = 0.28. Calculate P(C).
Show the worked answer
- The three outcomes cover every possibility, so their probabilities add to 1.
- P(A) + P(B) + P(C) = 1.
- 0.35 + 0.28 = 0.63.
- P(C) = 1 minus 0.63 = 0.37.
Common mistakes in this topic
- Using the wrong denominator, comparing one group with another instead of with the total.
- Giving a probability greater than 1.
- Confusing relative frequency with expected frequency.
- Rounding a fraction to a decimal early, which loses accuracy in later parts.
- Judging bias from a small number of trials.
Exam tips
- Leave probabilities as fractions unless the question asks otherwise. They stay exact through later parts.
- Check that every probability lies between 0 and 1 before writing it down.
- For not happening, use 1 minus the probability rather than recounting.
- Expected frequency means probability multiplied by trials, in that order.
- When commenting on fairness, refer to both the closeness of the values and the number of trials.
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Probability FAQs
How do I calculate the probability of an event?
Divide the number of favourable outcomes by the total number of possible outcomes. The total goes on the bottom, so a bag with 5 red counters out of 12 gives a probability of 5 over 12. Every probability lies between 0 and 1.
What is relative frequency?
The number of times an outcome occurred divided by the total number of trials. It is an experimental estimate of probability, and it becomes a more reliable estimate as the number of trials increases.
How do I find an expected frequency?
Multiply the probability of the outcome by the number of trials. If the probability of green is one third and there are 300 trials, the expected number is 100. This is an average expectation, so actual results will vary around it.
How do I tell whether a die or spinner is biased?
Compare the relative frequency from the experiment with the theoretical probability. If they are close, especially over a large number of trials, the object appears fair. A large difference over many trials suggests bias, but small differences are normal random variation.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.