ECZ 2016 · O-Level Paper 2 · Question 2 — Sets
Question from ECZ 2016 · O-Level Paper 2 · Question 2
(a) Of the 50 villagers who can tune in to Kambani Radio Station, 29 listen to news, 25 listen to sports, 22 listen to music, 11 listen to both news and sports, 9 listen to both sports and music, 12 listen to both news and music, 4 listen to all the three programmes, and 2 do not listen to any programme.
(a(i)) Draw a Venn diagram to illustrate this information.[2]
Verified working — step 1
Start at the centre: all three = 4.(a(ii)) How many villagers
(a(ii)(a)) listen to music only,[1]
Verified working — step 1
Music only = total music minus the three overlapping regions.(a(ii)(b)) listen to one type of programme only,[1]
Verified working — step 1
One programme only = News only + Sports only + Music only.(a(ii)(c)) listen to two types of programmes only?[1]
Verified working — step 1
Two programmes only = the three pairwise overlaps.(b) A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random
(b(i)) one tested negative while the other positive,[3]
Verified working — step 1
P(positive) = 0.6, so P(negative) = 1 - 0.6 = 0.4.(b(ii)) both patients tested negative.[2]
Verified working — step 1
P(negative) = 1 - 0.6 = 0.4 for each patient, independently.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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