In a group of 100 children, 64 children like to play cricket, 53 children like to play football and 20 children like to play both cricket and football. How many children do NOT like to play cricket or football ?
3
5
7
9
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2020
Let C be the set of children who like cricket and F be the set of children who like football.
Total children = 100.
Number of children who like cricket, |C| = 64.
Number of children who like football, |F| = 53.
Number of children who like both cricket and football, |C ∩ F| = 20.
The number of children who like at least one of the games (either cricket or football or both) is given by the union of the two sets:
|C U F| = |C| + |F| – |C ∩ F|
|C U F| = 64 + 53 – 20
|C U F| = 117 – 20
|C U F| = 97.
This means 97 children like either cricket or football or both.
The number of children who do NOT like to play cricket or football is the total number of children minus the number of children who like at least one game:
Children who like neither = Total children – |C U F|
Children who like neither = 100 – 97
Children who like neither = 3.
– Understand that the number of elements in the union represents those who like at least one of the items.
– Subtract the number who like at least one from the total number to find those who like neither.