Combined Events
Combined events involve finding the probability of two or more things happening together or in sequence. Students use the addition rule for OR and the multiplication rule for AND, applying these to independent and dependent events.
What You'll Learn
- Using sample space diagrams to list all outcomes
- Applying the addition rule for mutually exclusive events
- Applying the multiplication rule for independent events
- Distinguishing between independent and dependent events
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Adding probabilities when they should be multiplied (AND vs OR confusion)
Assuming events are independent when they are not
Not listing all possible outcomes in a two-way sample space
What Examiners Say About Combined Events
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Common Mistake●●●●●
In probability without replacement, the denominator DECREASES by 1 for each subsequent pick (13 → 12 → 11...). Getting 104/169 instead of the correct answer usually means you forgot this.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q25
- Common Mistake●●●●●
For 'exactly one green button' out of two picks, there are TWO orderings: green-then-not OR not-then-green. Calculate one product and DOUBLE it (or add both products).
Source: CIE 0580 · May/June 2023 · Paper 4 · Q15
- Technique●●●●●
In a histogram, bar HEIGHT = frequency density (frequency ÷ class width). Find the scale using a bar whose frequency AND width you know, then apply it to the others.
Source: CIE 0580 · Feb/March 2022 · Paper 4 · Q5b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Probability Basics
Basic probability introduces the scale from 0 to 1 and the idea of equally likely outcomes. Students calculate probabilities of single events, understand mutually exclusive events, and work with the probability that something does not happen.
Probability Trees
Tree diagrams organise multi-stage probability problems into a clear visual structure. Students multiply along branches for combined probabilities and add between branches for alternative outcomes.
Conditional Probability
Conditional probability deals with the likelihood of an event given that another event has already occurred. This topic uses tree diagrams, two-way tables and Venn diagrams to calculate P(A given B).
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Probability trees, Venn diagrams, and data guides