Question

the mathematics department of a college has 13 male professors, 9 female professors, 11 male teaching assistants, and 6 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male. the probability is \boxed{}. (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Calculate total number of people

Total people \(=13 + 9+11 + 6=39\)

Step2: Calculate number of professors

Number of professors \(=13 + 9 = 22\)

Step3: Calculate number of males

Number of males \(=13+11 = 24\)

Step4: Calculate number of male professors

Number of male professors \(=13\)

Step5: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event of selecting a professor and \(B\) be the event of selecting a male.
\(P(A)=\frac{22}{39}\), \(P(B)=\frac{24}{39}\), \(P(A\cap B)=\frac{13}{39}\)
\(P(A\cup B)=\frac{22 + 24-13}{39}=\frac{33}{39}=\frac{11}{13}\)

Answer:

\(\frac{11}{13}\)