ECZ 2024 · O-Level Paper 2 · Question 2 — Sets
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. 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.
(a(i)) Box A contains 2 green and 3 blue balls; Box B contains 4 green and 2 blue balls. One ball is selected at random from each box. What is the probability that both balls selected are blue?[2]
Verified working — step 1
P(blue from A) = 35and P(blue from B) = …(a(ii)) What is the probability that both balls selected are of different colours?[3]
Verified working — step 1
P(green from A, blue from B) = (25)(26) = 430(b(i)) Illustrate the textbook information in a Venn diagram.[2]
Verified working — step 1
Centre first: n(all three) = 10.(b(ii)(a)) How many learners collected none of the textbooks?[1]
Verified working — step 1
50 learners altogether and 46 collected at least one type, so 50 - 46 = …(b(ii)(b)) How many learners collected one type of textbook only?[1]
Verified working — step 1
One type only = 15 + 5 + 2 = …(b(ii)(c)) How many learners collected two types of textbooks only?[1]
Verified working — step 1
Exactly two types = 3 + 6 + 5 = …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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