ECZ 2024 · GCE Paper 2 · Question 1 — Probability

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. The Venn diagram shows the number of elements of sets P, Q and R: Q only = 12, Q∩P = x, R = x + 1 (R is a subset of P, disjoint from Q), P outside R and Q = 2x + 1.

(a(i)) Draw a tree diagram to illustrate this information.[2]

Verified working — step 1

Bag has 6 beads: 2 Red (R), 4 Green (G).

(a(ii)) Calculate the probability that the beads selected are of different colours.[3]

Verified working — step 1

Different colours means (R then G) or (G then R).

(b(i)) Find the value of x, such that n(P) = 18.[2]

Verified working — step 1

n(P) = (P∩Q) + R + (P outside R and Q)

(b(ii)) Find n(R)'.[1]

Verified working — step 1

With x=4: Q only=12, P∩Q=4, R=x+1=5, P outside R,Q=2x+1=9.

(b(iii)) Find n(R ∪ Q).[1]

Verified working — step 1

n(R∪Q) = R + (P∩Q) + (Q only) = 5 + 4 + 12 = …

(b(iv)) Find n(P ∩ Q)'.[1]

Verified working — step 1

n(P∩Q) = x = …

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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