In a survey of 125 students of class 10 in a school, 65 preferred to visit lumbini, 75 preferred to visit Pokhara and 25 preferred both places in their annual excursion. (I) show above information in a venn-diagram (ii) find number of students who liked neither of two places (iii) find the number of students who liked only Lumbini
I) The Venn diagram for the given information would look like this:
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| Lumbini |
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\ /
\ /
\ /
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\ /
\ /
\ /
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| Both |
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/ \
/ \
/ \
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/ \
/ \
/ \
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| Pokhara |
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II) To find the number of students who liked neither Lumbini nor Pokhara, we need to subtract the number of students who liked Lumbini, liked Pokhara, or liked both from the total number of students:
Total students = 125
Liked Lumbini = 65
Liked Pokhara = 75
Liked both = 25
Number of students who liked neither = Total students - Liked Lumbini - Liked Pokhara + Liked both
Number of students who liked neither = 125 - 65 - 75 + 25
Number of students who liked neither = 10
Therefore, 10 students liked neither Lumbini nor Pokhara.
III) To find the number of students who liked only Lumbini, we need to subtract the number of students who liked both from the number of students who liked Lumbini:
Liked Lumbini = 65
Liked both = 25
Number of students who liked only Lumbini = Liked Lumbini - Liked both
Number of students who liked only Lumbini = 65 - 25
Number of students who liked only Lumbini = 40
Therefore, 40 students liked only Lumbini.
(i) To show the above information in a Venn diagram, we will have three circles representing the sets: Lumbini, Pokhara, and the intersection of Lumbini and Pokhara (students who preferred both places).
Lumbini: 65
Pokhara: 75
Both Lumbini and Pokhara: 25
Let's draw the Venn diagram:
Lumbini (65) Pokhara (75)
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Both (25)
(ii) The number of students who liked neither of the two places can be calculated by subtracting the total number of students who preferred either Lumbini or Pokhara (including the intersection) from the total number of students in the survey:
Total students = 125
Students who preferred either Lumbini or Pokhara (including both) = Lumbini + Pokhara - Both
= 65 + 75 - 25
= 115
Students who liked neither of the two places = Total students - Students who preferred either Lumbini or Pokhara (including both)
= 125 - 115
= 10
So, there are 10 students who liked neither Lumbini nor Pokhara.
(iii) The number of students who liked only Lumbini can be calculated by subtracting the number of students who preferred both places from the number of students who preferred Lumbini:
Students who liked only Lumbini = Lumbini - Both
= 65 - 25
= 40
Therefore, there are 40 students who liked only Lumbini.