Unit 4: Statistics and Probability
Topic 4.6: Combined Events Questions
Practice 20 exam-style questions for IB Math AA 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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2026• Aimnova practice — 4.6.3
Events A and B are independent with P(A) = 0.7 and P(B) = 0.2. Find P(A ∩ B).
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2026• Aimnova practice — 4.6.1
P(A) = 0.45, P(B) = 0.35 and P(A ∩ B) = 0.15. Find P(A ∪ B).
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2026• Aimnova practice — 4.6.1
Events A and B are mutually exclusive with P(A) = 0.28 and P(B) = 0.34. Find P(A ∪ B) and P(A ∩ B).
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2026• Aimnova practice — 4.6.3
A and B are mutually exclusive with P(A) = 0.32 and P(B) = 0.41. Find P(A ∪ B).
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2026• Aimnova practice — 4.6.3
A fair die is rolled and a fair coin is tossed. Find the probability of a six and a head.
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2026• Aimnova practice — 4.6.1
Of 50 people surveyed, 30 like tea (T), 25 like coffee (C) and 10 like neither. Find how many like both.
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2026• Aimnova practice — 4.6.3
Explain the difference between mutually exclusive events and independent events.
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2026• Aimnova practice — 4.6.2
A spinner lands on red with probability 0.4. It is spun twice. Find the probability it lands on red exactly once.
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2026• Aimnova practice — 4.6.2
A bag has 4 red and 5 blue counters. Two are drawn without replacement. Find the probability they are different colours.
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2026• Aimnova practice — 4.6.2
A box has 6 working and 2 faulty bulbs. Two are tested without replacement. Find the probability at least one is faulty.
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2026• Aimnova practice — 4.6.2
A coin is biased so P(head) = 0.7. It is tossed twice. Find the probability of two heads and the probability of exactly one head.
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2026• Aimnova practice — 4.6.3
P(A) = 0.5, P(B) = 0.3 and P(A ∩ B) = 0.15. Determine whether A and B are independent.
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2026• Aimnova practice — 4.6.2
A student gets to school by bus with probability 0.8; otherwise they walk. If they take the bus, P(late) = 0.1; if they walk, P(late) = 0.35. Find the probability the student is late.
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2026• Aimnova practice — 4.6.1
In a group of 60, 35 own a dog, 28 own a cat and 12 own both. A person is chosen at random.
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2026• Aimnova practice — 4.6.1
In a Venn diagram, n(A) = 20, n(B) = 14, n(A ∩ B) = 6 and n(neither) = 5. Find the total number of elements.
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2026• Aimnova practice — 4.6.1
Two events have P(A) = 0.5, P(B) = 0.3 and P(A ∪ B) = 0.7. Find P(A ∩ B).
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2026• Aimnova practice — 4.6.3
P(A) = 0.45, P(B) = 0.4 and P(A ∩ B) = 0.25. Determine whether A and B are independent.
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2026• Aimnova practice — 4.6.3
A and B are independent with P(A) = 0.6 and P(B) = 0.5.
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2026• Aimnova practice — 4.6.1
In a class of 40, 22 study Spanish (S), 18 study French (F) and 9 study both.
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2026• Aimnova practice — 4.6.2
A bag has 5 green and 3 yellow sweets. Two are taken without replacement. Find the probability both are green.
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