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Venn diagrams and probability
Venn diagrams sort outcomes into overlapping groups, making probabilities easy to read.
Filling a Venn diagram
Start with the overlap (both), then each circle's remaining part, then the outside (neither). Check the total.
30 students: 18 like tea, 15 like coffee, 8 like both. Tea only 10, coffee only 7, both 8, neither 5.
30 students: 18 like tea, 15 like coffee, 8 like both. Tea only 10, coffee only 7, both 8, neither 5.
Reading probabilities
P(tea) = 1830. P(tea and coffee) = 830. P(neither) = 530.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Conditional from a Venn (Higher)
P(coffee given tea) = 818: restrict to the tea circle only.
From the tea and coffee example, find P(tea or coffee).
- Tea only + coffee only + both = 10 + 7 + 8 = 25
- 2530 = 56
Answer: 56
Fill a Venn diagram from the overlap outwards and check the total. Read P(A), P(A ∩ B) and P(neither) by counting regions over the total.
Check you have got it
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