Wassce Core Mathematics June 2019 Paper 2 Question10(a)

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Question10 (a) Core Mathematics June 2019 Paper 2 

In a class of 50 students. 24 like football, 21 basketball and 18 cricket. Six like football and basketball only, 3 like basketball only. 5 like all the three. games and 14 did not like any of the three games.

 

1. Illustrate this information on a Venn diagram.
2. Find the number of students who like:
   1. football and cricket only;
   2. exactly one of the games.

The Answer to Wassce Core Mathematics June 2019 Paper 2 Question 10 (a)

 

n(U)= 50 , n(F) = 24, n(B) = 21, n(C) =18,

n(F n B only) = 25, n(B only) = 3, n(F nB nC) = 5, n(F u B u C)’ = 14

Let n(F n C only) = x, n(B nC only) = y n(F only) = m, n(C only) = b

 

(i) The Venn diagram is shown below.

U (50)

 

 

 

 

 

 

(ii) From set B: 6+5+3+y= 21

14+ y = 21

y =7

 

n(C)+m+6+3+14 =50

18+m+6+3+14=50 nz + 41= 50

m =9

 

From set F:

m + 6+5 = 24

9+x+6+5 = 24 x+ 20 = 24 x =4

 

From set C: x+5+ y+n =18.

4+5+7+b=18 b+16=18 b = 2

 

(a) The number of students who like football and cricket only

From the above calculations the answer = 4

(b) The number of students who like Exactly one of the games

= 9+3+2 = 14

 

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