Answer
$\frac{13}{20}$
Work Step by Step
Step 1. The total number is $8+11+14+7=40$
Step 2. The probability of choosing a professor is
$P(prof)=\frac{8+11}{40}=\frac{19}{40}$
Step 3. The probability of choosing a female is
$P(female)=\frac{11+7}{40}=\frac{18}{40}$
Step 4. The probability of choosing a female professor is
$P(female\ prof)=\frac{11}{40}$
Step 5. The probability of choosing a professor or a female is
$P(prof\ or\ female)=P(prof)+P(female)-P(female\ prof)=\frac{19}{40}+\frac{18}{40}-\frac{11}{40}=\frac{26}{40}=\frac{13}{20}$
