ECZ 2023 · GCE Paper 2 · Question 3 — Probability

A girl has 7 green apples and 6 red apples in a bag. She picks one apple at random from the bag and eats it. She picks another apple and eats it.

(a) Express 91 - 4k- 81 - 3kas a single fraction in its simplest form.[3]

Verified working — step 1

Common denominator = (1-4k)(1-3k).

(b(i)) Draw a tree diagram to illustrate all the possible outcomes.[2]

Verified working — step 1

Bag starts with 7 green (G) and 6 red (R), total 13 apples.

(b(ii)) What is the probability that the first apple eaten was green?[3]

Verified working — step 1

The probability that the first apple eaten is green is simply the probability shown on the first branch of the tree diagram (before any second pick).

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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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