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?
5000
6000
6250
5400
Answer is Right!
Answer is Wrong!
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.