Questions
MTH-1235-001 - 51223 - 202505 Final Exam
Single choice
If a class of 40 students includes 18 who play basketball and 15 who play football, with 7 playing both, how many students play at least one of the sports?
Options
A.34
B.28
C.40
D.26
View Explanation
Verified Answer
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Step-by-Step Analysis
We start by identifying what the question asks: how many students play at least one of the two sports (basketball or football).
Option 1: 34. This would imply |A ∪ B| = 34. Using inclusion-exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| ......Login to view full explanationLog in for full answers
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Question text In a club of 25 students:- 14 play basketball- 12 play soccer- 6 play both sports Student 1:"I was asked to find how many students play only soccer. I subtracted: 12 – 6 = 6."Answer 1 Question 46[select: , The student is correct; subtracting overlap gives 6 students who play only soccer., The student is incorrect; they should have added, not subtracted. The correct answer is 18., The student is incorrect; only 3 play soccer, and 9 play both.] Student 2:"I was asked to find how many students play neither sport. I did 25 – 14 – 12 + 6 = 5."Answer 2 Question 46[select: , The student is incorrect; the answer should be 3 because overlap was double-counted., The student is incorrect; permutations should have been used instead, the correct value is 42., The student is correct; inclusion-exclusion correctly gives 5 students who play neither sport.] Student 3:"I was asked to find how many students play at least one sport. I did 14 + 12 = 26."Answer 3 Question 46[select: , The student is correct; 26 is accurate for at least one sport., The student is incorrect; the overlap must be subtracted. The correct total is 20., The student is incorrect; they should have used multiplication, and the total is 84.]
In a group of 50 students: - 20 like hiking - 25 like biking - 10 like both How many like either hiking or biking?
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