Cambridge IGCSE Maths Extended Probability Exam Questions
Cambridge IGCSE Mathematics 0580 Extended probability questions can involve notation, combined events and conditional probability. The 2025–2027 syllabus distinguishes Core from Extended material, so students should revise the content appropriate to their tier. A strong solution begins by defining events and identifying whether selections occur with or without replacement, before using tree diagrams or Venn diagrams.
Know the basic probability notation
P(A) means the probability of event A and P(A′) the probability that A does not occur. The complement rule is P(A′) = 1 − P(A). Thus if the probability of rain is 0.3, the probability of no rain is 0.7. Values must be between zero and one. In Extended questions, notation such as intersection and union may appear, and students should distinguish 'A and B' from 'A or B' clearly.
Further reading: KS3 Probability Explained With Everyday Examples
Work with dependent and independent events
For two independent events, the probability of both is obtained by multiplying their individual probabilities. For selections without replacement, the second probability can change depending on the first outcome. In a bag with 3 red and 2 blue counters, P(red then red) without replacement is 3/5 × 2/4 = 3/10. With replacement, the corresponding value is 3/5 × 3/5 = 9/25. Read the selection wording before filling tree branches.
Further reading: IGCSE Maths vs GCSE Maths: What Is Actually Different?
Use a complete tree diagram
Write first-stage probabilities that total one. At the next stage, update the counts if the earlier selection changes what remains. Multiply along each route. To find exactly one red in two selections without replacement from the bag, combine red-blue and blue-red, each with probability 3/10, giving 3/5. Check that all terminal routes sum to one. These checks are often quicker than trying to repair a final result that seems implausible.
Conditional probability in a clear example
For the same bag, if the first counter is known to be red and is not replaced, the probability of red on the second draw is 2/4 = 1/2. If the first is known to be blue, the probability of red second is 3/4. The condition changes the information available. The general idea behind P(A | B) is that we restrict attention to cases where B is true. A labelled sample space or tree can make this visible before using algebraic formulas.
Further reading: Maths Tutoring for KS3, GCSE, IGCSE and A-Level Students
Use Venn diagrams for overlapping events
When events can overlap, P(A or B) = P(A) + P(B) − P(A and B). The intersection is subtracted because it would otherwise be counted twice. For example, if P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.2, their union is 0.9. In a Venn diagram fill the overlap first, then the exclusive regions, and check the total probability adds to one.
Further reading: Unlocking the Secrets of Harder Quadratics: A Quick Trick for GCSE and IGCSE Success
Practise the language of exam questions
Distinguish 'at least one' from 'exactly one', and 'given that' from an ordinary unconditional probability. 'At least one' may be easier to solve using the complement of none. State each route or region clearly rather than supplying an unsupported number. Follow the current Cambridge syllabus for the correct tier, especially where Extended-only conditional probability is involved.
Further reading: GCSE Maths Surds: Simplifying and Rationalising Denominators
Frequently asked questions
Does Cambridge IGCSE Extended include conditional probability?
Yes, conditional probability is included in Extended content in the 2025–2027 0580 syllabus.
Can tree diagrams involve selection without replacement?
Yes. Extended combined-event problems may be with or without replacement.
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