The number of persons reading newspaper is shown in the following Venn Diagram (Survey of 50 persons):
[Venn Diagram showing numbers of persons reading Paper I, Paper II, and Paper III]
In a population of 10000, what is the number of persons expected to read at least two newspapers?
[amp_mcq option1=”5000″ option2=”6000″ option3=”6250″ option4=”5400″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2016
– Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons.
– Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons.
– Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons.
– Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons.
The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons.
The proportion of persons reading at least two newspapers in the sample is 21/50.
Expected number in a population of 10000 = (21/50) * 10000 = 0.42 * 10000 = 4200.
Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.