In a survey of a college it was found that 49% like reading maths , 52% like reading physics and 50% like ready chemistry and also, 20% like reading math and physics both , 21% like reading math and chemistry both and 23% like physics and chemistry both. If 5% like reading none of these 3 subjects ,then find out that what percentage of student like only one subject math , physics and chemistry?
Answers
Answer:
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Given : a survey of a college
To Find : what percentage of student like only one subject math , physics and chemistry
Solution:
n(M) = 49%
n(P) = 52 %
n(C) = 50 %
n( M ∩ P) = 20 %
n( M ∩ C) = 21 %
n ( P ∩C ) = 23 %
n( P ∩ M ∩ C) = ?
none = 5 %
Total = 100 %
=> Total = n(M) + n(P) + n(C) - n( M ∩ P) - n( M ∩ C) - n( C∩ P) + n( P ∩ M ∩ C) + none
=> 100 = 49 + 52 + 50 - 20 - 21 - 23 + n( P ∩ M ∩ C) + 5
=> n( P ∩ M ∩ C) = 8
n( P ∩ M ∩ C) = 8 %
Only maths = n(M) - n( M ∩ P) - n( M ∩ C) + n( P ∩ M ∩ C)
Only P = n(P) - n( M ∩ P) - n( P ∩ C) + n( P ∩ M ∩ C)
Only C = n(C) - n( M ∩ C) - n( P ∩ C) + n( P ∩ M ∩ C)
only one subject = n (M ) + n(P) + n(C) - 2 ( n( M ∩ P) + n( M ∩ C) + n( C∩ P) )
+ 3 n( P ∩ M ∩ C)
= 49 + 52 + 50 - 2(20 + 21 + 23) + 3 (8)
= 151 - 128 + 24
= 47
Hence 47 % of student like only one subject math , physics and chemistry
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