ECZ 2024 · GCE Paper 2 · Question 1 — Probability
Question from ECZ 2024 · GCE Paper 2 · Question 1
(a) A box contains 6 identical beads, 2 of which are red and the rest are green. Two beads are selected at random from the box, one after the other without replacement.
(a(i)) Draw a tree diagram to illustrate this information.[2]
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6 beads: 2 red and 4 green, drawn WITHOUT replacement.(a(ii)) Calculate the probability that the beads selected are of different colours.[3]
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"Different colours" happens two ways along the tree:(b) The Venn diagram shows the number of elements of sets P, Q and R. Find
(b(i)) the value of x, such that n(P) = 18,[2]
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Add up the regions inside P from the Venn diagram:(b(ii)) n(R)',[1]
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With x = 4 the regions are: Q only = 12, P∩Q = 4, R = 5, rest of P = 9.(b(iii)) n(R ∪ Q),[1]
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R ∪ Q is every element in R or Q or both, gathered once each:(b(iv)) n(P ∩ Q)'.[1]
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n(P ∩ Q) = x = …The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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