ECZ 2016 · O-Level Paper 2 · Question 2 — Sets
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 from the centre: n(all three) = 4.(a(ii)(a)) How many villagers listen to music only?[1]
Verified working — step 1
n(M only) = 22 - (8 + 4 + 5) = …(a(ii)(b)) How many villagers listen to one type of programme only?[1]
Verified working — step 1
n(N only) + n(S only) + n(M only) = 10 + 9 + 5 = …(a(ii)(c)) How many villagers listen to two types of programmes only?[1]
Verified working — step 1
7 + 5 + 8 = …(b(i)) A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. Two patients are selected at random. What is the probability that one tested negative while the other tested positive?[3]
Verified working — step 1
P(positive) = 0.6, so P(negative) = 1 - 0.6 = 0.4.(b(ii)) What is the probability that both patients tested negative?[2]
Verified working — step 1
P(both negative) = 0.4 x 0.4 = …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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