Question Answer - 1

Soalan daripada kawan saya:

Solution:

Question (a)
We know that total number of students is 35 but n(A∪B∪C) ≠ 35.

There are three students who did not choose any subject. 
So, we have n(A∪B∪C)' = 3. Then

n(A∪B∪C) = 35-3 =32

From the first three rows, we know that 

n(A) = 17, n(B) = 15 and n(C) = 21

The forth, fifth and sixth rows have word "and" which means "intersection" represents by this symbol ∩. From the information, we know that

n(A∩B) = 10, n(B∩C) = 11 and n(A∩C) = 9

Question (b)

Number of students who chose all three subjects = n(A∩B∩C). 

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C)
                       - n(A∩C) + n(A∩B∩C)
aaaaaaaa32 = 17 + 15 + 21- 9 - 11 - 10 + n(A∩B∩C)
n(A∩B∩C) = 9

There are nine students who chose all three subjects.

Question (c)
No. of students chose who Anthropology only 

= n(A) - n(A∩B) - n(A∩C) 
   + n(A∩B∩C)

= 17 - 9 - 10 + 9

= 7

Question (d)

No. of students who have two favorite subjects 

= [n(A∩B) - n(A∩B∩C)] 
     + [n(B∩C) - n(A∩B∩C)] 
     + [n(A∩C) - n(A∩B∩C)]
= (10 - 9) + (11 - 9) + (9 - 9)
= 1 + 2 + 0 
= 3