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.
What You'll Learn
- Calculating probability as favourable outcomes divided by total outcomes
- Understanding the probability scale from 0 (impossible) to 1 (certain)
- Using P(not A) = 1 - P(A)
- Listing outcomes systematically using sample spaces
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Giving a probability greater than 1 or less than 0
Not listing all possible outcomes in the sample space
Confusing theoretical probability with experimental (relative frequency)
What Examiners Say About Probability Basics
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 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.
Venn Diagrams
Venn diagrams represent sets and their overlaps visually, making them a powerful tool for probability and data classification. Students use them to organise information, find probabilities, and understand set notation including union, intersection and complement.
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.
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Probability trees, Venn diagrams, and data guides