32/37
Explanation:male professors = 5
female professors = 7
male teaching assistants = 16
female teaching assistants = 9
Total = 5 + 7 + 16 + 9
Total = 37
[tex]\begin{gathered} N(T.A\text{ or F) = N(T.A) + N(F) -N(T.A and F)} \\ T.A\text{ = teach i}ng\text{ assistant} \\ F\text{ = female} \end{gathered}[/tex][tex]\begin{gathered} N\text{ (T.A) }=\text{ }16\text{ + 9 = 25} \\ N(F)\text{ = 7 +9 = 1}6 \\ N(T.A\text{ and F) = }9 \\ N(T.A\text{ or F) = 25 + 16 - }9 \\ N(T.A\text{ or F) }=\text{ 3}2 \end{gathered}[/tex][tex]\begin{gathered} \text{Probability of teach i}ng\text{ assistant or a female = }\frac{N(T.A\text{ or F)}}{\text{Total}} \\ \text{Probability of teach i}ng\text{ assistant or a female =}\frac{32}{37} \end{gathered}[/tex]