Question

The physics department of a college has 5 male professors, 7 female professors. 16male teaching assistants and 9 female teaching assistants. If a person is selected atrandom from the group, find the probability that the selected person is a teachingassistant or a female.

Answer 1

32/37

Step-by-step explanation:

male professors = 5

female professors = 7

male teaching assistants = 16

female teaching assistants = 9

Total = 5 + 7 + 16 + 9

Total = 37

`\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}`
`\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}`
`\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 =}(32)/(37) \end{gathered}`