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Calculate probabilities using tree diagrams, Venn diagrams, combined events, and conditional probability.
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.
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 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 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.
Conditional probability deals with the likelihood of an event given that another event has already occurred. This higher-tier topic uses tree diagrams, two-way tables and Venn diagrams to calculate P(A given B).
Expected outcomes use probability to predict how many times an event should occur over a number of trials. Students multiply probability by the number of trials and compare expected results with experimental data.
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
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.
“There were very few candidates who did not recognise the significance of the lack of replacement of the first counter, although where this was an issue some still gained credit for an answer of 104/169 with others compounding their error by missing some of the required pairs.”
Source: CIE 0580 · June 2024 · Paper 2 · Q25
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).
“Most recognised the need to start off with 5/13 for the probability of a first button being green, which earned a first method mark. Many fewer were able to use this correctly in a product with 8/12 for a second button being non-green to score the next mark. Only the stronger candidates realised that they also needed to double the result of the product to account for the possibility of green being the second button.”
Source: CIE 0580 · November 2023 · Paper 4 · Q15
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.
“This proved challenging for many. Those answers displaying understanding that the heights of the blocks of a histogram represented the frequency densities usually had no difficulty. Some clearly showed the calculation of the scale factor for the first bar as 17.2 ÷ 0.86 = 20 and used this correctly with the remaining frequency densities.”
Source: CIE 0580 · June 2022 · Paper 4 · Q5b
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
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