#### Answer

$\frac{4}{5}$

#### Work Step by Step

If A and B are not mutually exclusive events, then
P(A or B) = P(A)+P(B) - P(A and B)
We are asked to find the probability that a randomly selected person on the faculty is a teaching assistant or a female.
P(choosing a teaching assistant) = $\frac{No. Of teaching assistant}{Total Faculty }$ =$\frac{21}{40}$
P(choosing a female)= $\frac{No. of females}{Total Faculty}$ = $\frac{18}{40}$
P(a TA and a female) = $\frac{7}{40}$
P(a TA or a female) = P(a TA) +P(a female) - P(a TA and a female)
=$\frac{21}{40}$ + $\frac{18}{40}$ - $\frac{7}{40}$
=$\frac{21+18 -7}{40}$ = $\frac{32}{40}$ = $\frac{4}{5}$