Question

The mathematics department of a college has 6 male professors, 9 female professors, 5 male teaching assistants, and 6 female teaching assistants. If a personselected at random from the group, find the probability that the selected person is a teaching assistant or a female.

Answer 1

Given:

6 male professores

9 female professores

5 male teaching assistants

6 female teaching assistants

Sol:.

`N(A\text{ or B)=N(A)+N(B)-N(A and B)}`

N (professors)

`\begin{gathered} =6+9 \\ =15 \end{gathered}`

N(Male)

`\begin{gathered} =6+5 \\ =11 \end{gathered}`

N(professors and male)

`=6`

N(professors OR male) = N(professors) + N(males) -N(professor OR male)

`\begin{gathered} N(\text{ Professors OR male)=15+11-6} \\ =20 \end{gathered}`

N(People to choose from)

`\begin{gathered} =6+9+5+6 \\ =26 \end{gathered}`

Then probablitiy is:

`\begin{gathered} =(20)/(26) \\ =(10)/(13) \end{gathered}`

Then the probability is 10/13