in a survey of 100 students, the number of students studying the various languages were found to be: english only 18, english but not hindi 23, englsih and sanskrit 8, english 26, sanskrit 48, sankrit and hindi 8, no launguage 24. find how many students were studying: (1) hindi (2) english and hindi (#) exactly one language (4)all 3 launguages (5)at least two of these languages (6) exactly 2 languages.

Asked by PriyaAnk ShaRma | 27th Jun, 2013, 12:32: PM

Expert Answer:

Let E, H and S denote the set of students who are studying English, Hindi and Sanskrit respectively.

Then, n (?) = 100

n (E) = 26

n (S) = 48

n (E ? S) = 8

n (S ? H) = 8

From the Venn-Diagram, it is clear that- n (E ? H ? S) = 3

The number of students who study English only = 18

Number of students who study no language = 24

? Number of students who study Hindi only = [100 – (18 + 5 + 3 + 5 + 35)] – 24

= 100 – 66 – 24

= 100 – 90

= 10

? Number of students who study Hindi

= 10 + 3 + 5

= 18

and Number of students who study English and Hindi = 3

3. Number of students who studies exactly one language = 18+35+10 = 63
 
4. All 3 languages n (E ? H ? S) = 3
 
5. at least 2 languages = n (E ? H) + n (E ? S) +n (H ? S) + n (E ? H ? S)
= 0+5+5+3 = 13
 
6. exactly 2 langauges = n (E ? H) + n (E ? S) +n (H ? S) 
= 0+5+5 = 10
 
So, yes the question is correct, except that here n (E ? H) = 0, which is not something that is always intutive from a venn diagram. 
 
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Answered by  | 27th Jun, 2013, 06:22: PM

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