ECZ 2017 · GCE Paper 2 · Question 3 — Probability

Question from ECZ 2017 · GCE Paper 2 · Question 3

(a) In a box of 10 bulbs, 3 are faulty. If two bulbs are drawn at random one after the other, find the probability that

(a(i)) both are good,[2]

Verified working — step 1

10 bulbs, 7 good, drawn one after the other WITHOUT replacement.

(a(ii)) one is faulty and the other is good.[3]

Verified working — step 1

"One faulty and one good" is faulty-then-good or good-then-faulty.

(b) The Venn diagram below shows tourist attractions visited by students in a certain week.

(b(i)) Find the value of y, if 7 students visited Mambilima Falls only.[2]

Verified working — step 1

The Mambilima-only region is 2y + 1, and that equals 7.

(b(ii)) How many students visited

(b(ii)(a)) Victoria Falls but not Gonya Falls,[1]

Verified working — step 1

Victoria but not Gonya = (Victoria only) + (Victoria and Mambilima only).

(b(ii)(b)) two tourist attractions only,[1]

Verified working — step 1

Two attractions only = the three pairwise overlaps.

(b(ii)(c)) one tourist attraction only?[1]

Verified working — step 1

One attraction only = Victoria only + Mambilima only + Gonya only.

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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