Question

22. In a class of 75 students, the following observations
were made : 40 play cricket, 35 play hockey, 30 play
football, 15 play both cricket and hockey. 10 play both
hockey and football, 12 play both cricket and football,
play all the three games. Draw a Venn diagram
showing these sets and find
(i) the number of students who play either hockey
or cricket
(ii) the number of students not playing any game ​

Answer 1

Answer

1) 45 student play hockey or cricket.

2) 0 student not playing any games.

Answer 2

The number of students following exactly two of three games

∑n(A∩B) = 18

the number of students not playing any game ​are 5

explanation:

Number of students who follow cricket n(A) = 40

Number of students who follow hockey n(B) = 35

Number of students who football follow  n(C) = 35

Number of students who follow all three games (A∩B) = 15

Number of students who follow all three games (A∩C) = 12

From Venn diagram we know,

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

75 = n(A) + n(B) + n(C) - ∑ n(A∩B) + 5

75 = 40 + 38 + 10 - ∑n(A∩B) + 5

∑n(A∩B) = 93 - 75 = 18

n(A∩B) + n(B∩C) + n(C∩A) = 18

So, the number of students following exactly two of three games

∑n(A∩B) = 18

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