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In a group of 60 students, 38 play basketball, 35 play hockey and 5 do not play either basketball or hockey - HSC - SSCE Mathematics Advanced - Question 2 - 2024 - Paper 1

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In a group of 60 students, 38 play basketball, 35 play hockey and 5 do not play either basketball or hockey. How many students play both basketball and hockey? A. ... show full transcript

Worked Solution & Example Answer:In a group of 60 students, 38 play basketball, 35 play hockey and 5 do not play either basketball or hockey - HSC - SSCE Mathematics Advanced - Question 2 - 2024 - Paper 1

Step 1

Calculate students playing either basketball or hockey

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Answer

First, we know that 5 students do not play either sport. Thus, the number of students who play either basketball or hockey is:

$60 - 5 = 55$ .

Step 2

Use the principle of inclusion-exclusion

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Answer

Let:

B = number of students who play basketball = 38
H = number of students who play hockey = 35
x = number of students who play both sports

Using the formula for the union of two sets: $|B ext{ or } H| = |B| + |H| - |B ext{ and } H|$ We substitute: $55 = 38 + 35 - x$ .

Now, we solve for x: $55 = 73 - x$ $x = 73 - 55$ $x = 18$ .

Step 3

Conclusion

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Answer

Thus, the number of students who play both basketball and hockey is 18.

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