A) 3300
B) 3200
C) 3000
D) 3400
Correct Answer: A
Solution :
[3300]| \[n(A)=40\,percent\,\,of\,\,10,000=4,000\] |
| \[n(B)=20\,percent\,\,of\,\,10,000=2,000\] |
| \[n(C)=10\,percent\,\,of\,\,10,000=1,000\] |
| \[n(A\cap B)=5\,percent\,\,of\,\,10,000=500\] |
| \[n(B\cap C)=3\,percent\,\,of\,\,10,000=300\] |
| \[n(C\cap A)=4\,percent\,\,of\,\,10,000=400\] |
| \[n(A\cap B\cap C)=2\,percent\,\,of\,\,10,000=200\] |
| Number of families which buy newspaper A only |
| \[=n(A\cap {{B}^{c}}\cap {{C}^{c}})\] |
| \[=n[(A\cap {{B}^{c}}\cup {{C}^{c}})]\] |
| \[=[n(A)-n[A\cap (B\cup C)]\] |
| \[=[n(A)-n[(A\cap B)\cup (A\cap C)]\] |
| \[=[n(A)-[n(A\cap B)+n(A\cap C)-n(A\cap B\cap C)]\] |
| \[=4000-[500+400-200]\] |
| \[=4000-700=3300\] |
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