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

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 $\frac{99}{428}$ and students who only like football is $\frac{101}{428}$ . All you need to do is add these fractions together to get your answer.

$\frac{99}{428} +\frac{101}{428} =\frac{200}{428}$

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