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19 Dec 2025

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GCSE Maths: Probability and Set Notation Notes

esther

@esther_hzdf

Probability and set theory might seem tricky at first, but... Show more

UNION
AUB EITHER A OR B OR BOTH
MUTUALLY EXCLUSIVE
OO
NO INTERSECTION
PROBABILITY FACTS
Pr (A)= NO. FAVOURED OUTCOMES
NO. POSSIBLE OUTCOMES

Set Operations and Probability Essentials

Understanding set operations is like learning a new language for describing groups and overlaps. The union (A∪B) means "either A or B or both" - think of it as everything that belongs to at least one group. The intersection (A∩B) is much stricter - it's only the stuff that's in both groups at the same time.

When you see A' (called "A complement"), that's everything that's NOT in group A. This connects directly to probability: if the chance of something happening is Pr(A), then the chance it doesn't happen is Pr(A') = 1 - Pr(A). Dead simple once you get it!

Mutually exclusive events can never happen at the same time - like rolling a 3 and a 5 on the same die. When events are mutually exclusive, Pr(A∩B) = 0 because there's no overlap possible.

Top Tip: When shading Venn diagrams, shade all the required bits for A and B separately first. For union, keep everything shaded. For intersection, only keep the overlapping bits!

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1 page

GCSE Maths: Probability and Set Notation Notes

esther

@esther_hzdf

Probability and set theory might seem tricky at first, but they're actually just fancy ways of describing everyday situations where you're dealing with groups of things and chances of events happening. This guide breaks down all the essential formulas and... Show more

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Set Operations and Probability Essentials

Mutually exclusive events can never happen at the same time - like rolling a 3 and a 5 on the same die. When events are mutually exclusive, Pr(A∩B) = 0 because there's no overlap possible.

Top Tip: When shading Venn diagrams, shade all the required bits for A and B separately first. For union, keep everything shaded. For intersection, only keep the overlapping bits!