Question

There are 100 boys in a sports club. 65 of them play soccer, 50 play hockey, and 40 play basketball. 25 play soccer and hockey, 20 play hockey and basketball, and 5 play all three games. Each boy plays at least one of the three games. Draw a Venn diagram to illustrate this information. Find the number of boys who play:

a. Only basketball

b. Only soccer

c. Exactly two games

A. a. 20, b. 40, c. 35

B. a. 25, b. 45, c. 30

C. a. 30, b. 35, c. 25

D. a. 15, b. 50, c. 20

Answer 1

Using a Venn diagram, the number of boys who play only basketball is 15, only soccer, is 35 and exactly two games is 50.

This Venn diagram has intersecting circles representing soccer, hockey, and basketball. The overlapping circles represent the boys who play more than one game.

Let the number of boys who play soccer = s

Let the number of boys who play hockey = h

Let the number of boys who play basketball = b

The number of boys who play soccer = 65

The number of boys who play hockey = 50

The number of boys who play basketball = 40

The number of boys who play soccer and hockey = 25

The number of boys who play hockey and basketball = 20

The number of boys who play all three games = 5

a. Only basketball: The number of boys who play only basketball = 15 (40 - 20 - 5)

b. Only soccer: The number of boys who play only soccer = 35 (65 - 25 - 5)

c. Exactly two games: This is the sum of the boys in the intersections of the circles (S ∩ H, H ∩ B, S ∩ B). Number of boys = 50 (25 + 20 + 5)

Thus, the number of boys who play only basketball is 15, who play only soccer is 35, and who play exactly two games is 50.