ECZ 2024 · O-Level Paper 2 · Question 2 — Sets
Question from ECZ 2024 · O-Level Paper 2 · Question 2
(a) Two boxes A and B contain balls of the same size. Box A contains 2 green balls and 3 blue balls while Box B contains 4 green balls and 2 blue balls. If one ball is selected at random from each box, what is the probability that both balls selected are
(a(i)) blue,[2]
Verified working — step 1
Box A: P(blue) = 35. Box B: P(blue) = 26.(a(ii)) of different colours?[3]
Verified working — step 1
"Different colours" happens two ways:(b) On a particular day at a school with 50 Grade 12 learners, 33 collected Biology textbooks, 24 collected Mathematics textbooks and 23 collected History textbooks from the school library. 13 learners collected both Biology and Mathematics textbooks, 16 collected both Mathematics and History textbooks, 15 collected both Biology and History textbooks and 10 collected all the three types of textbooks.
(b(i)) Illustrate this information in a Venn diagram.[2]
Verified working — step 1
Fill from the CENTRE outwards: all three = 10.(b(ii)) How many learners collected
(b(ii)(a)) none of the textbooks,[1]
Verified working — step 1
46 learners collected at least one type…(b(ii)(b)) one type of textbook only,[1]
Verified working — step 1
"One type only" is the thr…(b(ii)(c)) two types of textbooks only?[1]
Verified working — step 1
"Exactly two types" is th…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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