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Details Of the Wassce Core Mathematics 1993 Question 21
In a Senior Secondary School, there are 174 students in Form 2. Of these, 86 play table tennis, 84 play football, 94 play volleyball; 30 play table tennis and volleyball, 34 play volleyball and football and 42 play table tennis and football. Each student plays at least one of the three games and x students play all three games.
- Display these facts in a Venn diagram.
- Write down an equation in x and hence find
- If a student is chosen at random from Form 2, what is the probability that he plays two games?
The answer To Wassce Core Mathematics 1993 Question 21
n(U) =174 , n(T) = 86, n(F) = 84, n(V) = 94, n(T nV) = 30, n(F nV) = 34, n(T nV) = 42.
a. The Venn diagram is shown below:
b. From the Venn diagram,
Number of students who play Table tennis only, a = 86—(30—x+x+42—x) =14+x
Furthermore, the number of students who play Football only, b=84—(42—x+x+34—x) =8+x
Also, the number of students who play Volleyball only, c=94—(30—x+x+34—x) =30+x
n(T ∪F ∪V)= n(U)
(14+x)+(8+x)+(30+x)+x+(42—x)+ (30—x) + (34—x) =174 158+x=174
The ans is 16 students
(c) Number of students who play two games
= (42—x) + (30—x) + (34—x)
= (42 —16) + (30 —16) + (34 –16)
⸫ Probability that a student plays two games
58/173 = 1/3
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