402 students were surveyed about their preferences of sports. 140 students like football, 144 students like baseball, and 42 students like both sports. How many students like exactly one of the two sports?
a) 200
b) 140
c) 284
d) 98
e) 102
140 + 144 + 42 = 326
What about the remaining 76 students?
140 + 144 = ?
To find the number of students who like exactly one of the two sports, we need to subtract the number of students who like both sports (42) from the total number of students who like either football or baseball.
Let's calculate that:
Number of students who like football only = Number of students who like football - Number of students who like both sports
= 140 - 42
= 98
Number of students who like baseball only = Number of students who like baseball - Number of students who like both sports
= 144 - 42
= 102
Therefore, the total number of students who like exactly one of the two sports is 98 + 102 = 200.
So, the correct answer is option a) 200.
To find the number of students who like exactly one of the two sports, we can use the principle of inclusion-exclusion.
Let's break down the given information:
- Number of students who like football = 140
- Number of students who like baseball = 144
- Number of students who like both football and baseball = 42
To find the number of students who like exactly one of the two sports, we need to subtract the number of students who like both sports from the total number of students who like football and baseball combined.
Total number of students who like football or baseball = Number of students who like football + Number of students who like baseball
Total number of students who like football or baseball = 140 + 144 = 284
However, this count includes the students who like both sports. We need to subtract those students to get the correct count.
Number of students who like exactly one of the two sports = Total number of students who like football or baseball - Number of students who like both sports
Number of students who like exactly one of the two sports = 284 - 42 = 242
Therefore, the correct answer is not listed among the options.