Question

428 students were surveyed about their preferences of sports. 146 students like football, 144 students like baseball, and 45 students like both sports. how many students like exactly one of the two sports?

Answer 1

To determine how many students like exactly one of the two sports (football or baseball), we apply the principle of inclusion-exclusion. By adding the numbers who like each sport and subtracting those who like both, we find that 245 students like exactly one sport.

Step-by-step explanation:

The student is asking how many students like exactly one of the two sports, given that 428 students were surveyed, 146 like football, 144 like baseball, and 45 students like both sports. To find the number of students who like exactly one sport, we can use the principle of inclusion-exclusion. We start by adding the number of students that like each sport, and then subtract the number who like both, since they are counted twice.

Step-by-step calculation:

Students who like football: 146

Students who like baseball: 144

Students who like both sports: 45

Students who like exactly one sport: (146 + 144) - 45 = 245

Therefore, 245 students like exactly one of the two sports, either football or baseball.

Answer 2

This is what we already know:

`\left[\begin{array}{cccc} &YB&NB&total\\YF&45&[unknown]&146\\NF&[unknown]&[unknown]&[unknown]\\total&144&[unknown]&428\end{array}\right]`

And using this information, we can fill the table out. Remember that everything must add up to the total in the column and row. The complete table looks like this:

`\left[\begin{array}{cccc} &YB&NB&total\\YF&45&101&146\\NF&99&183&282\\total&144&284&428\end{array}\right]`

Using the complete table, we see the fraction for students that only like baseball is
`(99)/(428)` and students who only like football is
`(101)/(428)` . All you need to do is add these fractions together to get your answer.

`(99)/(428) +(101)/(428) =(200)/(428)`

In short, 200 students only like one of the two sports.