Question

In a group of 100 children ,32%play hockey,64%play football and 40% paly cricket.14%play hockey and football, 15%play football and cricket and 13% play hockey and cricket.Only 6% paly all three games.
1).How many children play only one game?
2).How many children play atleast two games?
3).How many children play hockey and football but not cricket?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

1) The number of children who play only one game =  70

2) The number of children who play at least two games = 30

3) The number of children who play hockey and football but not cricket = 60

Step-by-step explanation:

Given,

Total number of children = 100

Since 32% play hockey, the number of children who play hockey = 32

Since 64% play football, the number of children who play football = 64

Since 40% play cricket, the number of children who play cricket = 40

Since 14% play hockey and football, the number of children who play hockey and football = 14

Since 15%play football and cricket, the number of children who play foot ball and cricket = 15

Since 13% play hockey and cricket, the number of children who play hockey and cricket = 13

Since 6% play all the games, the number of children who play all the games = 6

The number of children who play only hockey and football = 14-6 = 8

The number of children who play only hockey and cricket = 13-6 = 7

The number of children who play only football and cricket = 15 -6 = 9

The number of children who play only hockey = 32 - 8 -7 -6 = 11

The number of children who play only football = 64 - 8-6-9 = 41

The number of children who play only cricket  = 40 - 7-6-9 = 18

We can represent the below sets in the Venn diagram as follows. In the Venn diagram 'H' represents the children who play Hockey, 'C' represents the children who play 'Cricket' and 'F' represents the children who play football.

1) The number of children who play only one game = 11+41+18 = 70

2) The number of children who play at least two games = 7+8+9+6 = 30

3) The number of children who play hockey and football but not cricket = 11+8+41 = 60

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