As part of a survey, 35 students were asked if they like Rihanna (R) or One Direction (D) - Junior Cycle Mathematics - Question 6 - 2014
Question 6
As part of a survey, 35 students were asked if they like Rihanna (R) or One Direction (D). Some of the results are shown in the Venn diagram below.
(i) Complete the... show full transcript
Worked Solution & Example Answer:As part of a survey, 35 students were asked if they like Rihanna (R) or One Direction (D) - Junior Cycle Mathematics - Question 6 - 2014
Step 1
Complete the Venn diagram.
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Answer
To complete the Venn diagram, we need to find the number of students who like neither musician. We know:
The total number of students surveyed: 35
Students liking only Rihanna (R): 9
Students liking only One Direction (D): 6
Students liking both (R ∩ D): 12
Let’s calculate:
Total students liking either R or D:
9(R)+12(RD)+6(D)=27
Students liking neither:
35−27=8
Thus, we fill the Venn diagram as follows:
Students only liking Rihanna: 9
Students only liking One Direction: 6
Students liking both: 12
Students liking neither: 8
Step 2
How many pupils liked One Direction?
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Answer
To find the total number of pupils who liked One Direction, we sum the students who like only One Direction and those who like both:
Shade the region of the Venn diagram which represents R \ D.
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Answer
The region that represents R \ D consists of those who like Rihanna but not One Direction. To visually represent this, you shade the area of the Venn diagram that corresponds to the number 9 in the circle representing R, excluding the intersecting part with D.
Step 4
Describe in your own words what this shaded region represents.
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Answer
The shaded region represents the students who liked Rihanna but not One Direction. In other words, these are students who have a preference for Rihanna while not having any inclination towards One Direction.
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