Question:
In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is
In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is
Updated On: Jul 5, 2022
- 3100
- 3300
- 2900
- 1400
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The Correct Option is B
Solution and Explanation
$n(A) = 40\% \,of\, 10,000 = 4,000$
$n(B) = 20\% \,of\, 10,000 = 2,000$
$n(C) = 10\% \,of\, 10,000 = 1,000$
$n(A\cap B) = 5\% \,of\, 10,000 = 500$
$n(B\cap C) = 3\% \,of\, 10,000 = 300$
$n(C \cap A) = 4\% of \,10,000 = 400$
$n(A\cap B \cap C) = 2\% \,of\, 10, 000 = 200$
We want to find $n(A\cap B^c \cap C^c ) = n[A\cap (B\cup C)^c ]$
$= n(A) - n[A \cap (B \cup C)]$
$= n(A) - n[(A\cap B)\cup (A\cap C)]$
$= n(A) -[n(A\cap B) + n(A\cap C) - n(A\cap B\cap C)]$
$= 4000 - [500 +400 - 200] = 4000 - 700 = 3300$.
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".