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 the places in their annual excursion.

With the above information, do:

(i) Show the above information in a Venn-diagram

(ii) Find the number of students who liked neither of two places.

(iii) Find the number of students who liked only Lumbini.

Answer: (i) -, (ii) 10, (iii) 40

Solution:

Let U be the set of total students surveyed. Let L and P represent the set of students who liked to visit Lumbini and Pokhara, respectively.

Given,

$n(U) = 125$

$n(L) = 65$

$n(P) = 75$

$n(L \cap P) = 25$

To find:

(i) $n( \overline{ L \cup P})= ?$

(ii) $n_o(L) = ?$

We know,

$n(U) = n(L) + n(P) - n(L \cap P) + n(\overline{L \cup P})$

$or, 125 = 65 + 75 - 25 +n(\overline{L \cup P})$

$or, 125 = 140 - 25 + n(\overline{L \cup P})$

$or, 125 = 115 + n(\overline{L \cup P})$

$or, n(\overline{L \cup P}) = 125 - 115$

$\therefore n(\overline{L \cup P})= 10$

And,

$n_o(L) = n(L) - n(L \cap P)$

$or, n_o(L) = 65 - 25$

$\therefore n_o(L) = 40$

Hence,

The number of students who liked neither of two places were 10.

The number of students who liked only Lumbini were 40.

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