This is what we already know:
[tex] \left[\begin{array}{cccc} &YB&NB&total\\YF&45&[unknown]&146\\NF&[unknown]&[unknown]&[unknown]\\total&144&[unknown]&428\end{array}\right] [/tex]
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:
[tex] \left[\begin{array}{cccc} &YB&NB&total\\YF&45&101&146\\NF&99&183&282\\total&144&284&428\end{array}\right] [/tex]
Using the complete table, we see the fraction for students that only like baseball is [tex] \frac{99}{428} [/tex] and students who only like football is [tex] \frac{101}{428} [/tex] . All you need to do is add these fractions together to get your answer.
[tex] \frac{99}{428} +\frac{101}{428} =\frac{200}{428} [/tex]
In short, 200 students only like one of the two sports.
