Unit 4: Statistics and Probability
Topic 4.6: Venn Diagrams and Combined Events Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.6. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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A coin is tossed twice. Find the probability of two heads.
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A bag has 3 red and 7 white balls. Two are drawn WITH replacement. Find P(both red).
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From the Venn diagram (A only = 7, both = 3, B only = 5, neither = 5), find the total number of outcomes.
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Explain the difference between drawing WITH replacement and WITHOUT replacement.
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Two events along tree paths give P(A and late) = 0.18 and P(B and late) = 0.14. Find P(late).
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On a Venn diagram, what does the intersection region of sets A and B represent?
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A Venn diagram for A and B has P(A only) = 0.25, P(both) = 0.15, P(B only) = 0.30. Find P(neither).
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State what the notation A′ (A complement) means on a Venn diagram.
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40 people are surveyed; 25 like tea, 18 like coffee, 10 like both. Find how many like tea only.
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On a Venn diagram, what does the union of A and B represent?
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A Venn diagram has: A only = 7, both = 3, B only = 5, neither = 5. Find n(A).
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On a tree diagram, how do you find the probability of a sequence of events along one path?
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In a three-set Venn diagram, what does the central region (where all three circles overlap) represent?
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From the Venn diagram (A only = 7, both = 3, B only = 5, neither = 5), find n(A ∪ B).
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On a tree diagram, the two branches from one point are ''yellow'' with P = 0.3 and ''not yellow''. Find P(not yellow).
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Write down the conditional probability formula for P(A given B).
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P(A ∩ B) = 0.2 and P(B) = 0.5. Find P(A | B).
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A bag has 3 red and 7 white balls. Two are drawn WITHOUT replacement. Find P(both red).
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In a Venn diagram with 20 outcomes, the region outside both circles has 5 outcomes. Find P(A ∪ B).
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40 people: 25 like tea, 18 like coffee, 10 like both. Find how many like neither.
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