Step 1

a) The probability that it is a male or in managerial position is:

P(male or managerial position)

\(\displaystyle={\frac{{{n}{\left(\text{male or managerial position}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}\)

\(\displaystyle={\frac{{{n}{\left({m}{a}le\right)}+{n}{\left(\text{managerial position}\right)}-{n}{\left(\text{male and managerial position}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}\)

\(\displaystyle={\frac{{{44}+{12}-{8}}}{{{88}}}}\)

\(\displaystyle={\frac{{{6}}}{{{11}}}}\)

Step 2

b) The probability that it is neither male nor in managerial position is:

\(\displaystyle{P}{\left({m}{a}le\cap\text{managerial position}\right)}\)

\(\displaystyle={P}{\left(\text{male}\cup\text{managerial position}\right)}\)

\(\displaystyle={1}-{P}{\left({m}{a}le\cup\text{managerial position}\right)}\)

\(\displaystyle={1}-{P}{\left(\text{male or managerial position}\right)}\)

\(\displaystyle={1}-{\frac{{{6}}}{{{11}}}}\)

\(\displaystyle={\frac{{{5}}}{{{11}}}}\)

Step 3

c) The probability that it is female or clerical portion is:

P(female or clerical portion)

\(\displaystyle={\frac{{{n}{\left(\text{female or clerical portion}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}\)

\(\displaystyle={\frac{{{n}{\left({f}{e}{m}{a}le\right)}+{n}{\left(\text{clerical portion}\right)}-{n}{\left(\text{female and clerical portion}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}\)

\(\displaystyle={\frac{{{44}+{43}-{28}}}{{{88}}}}\)

\(\displaystyle={\frac{{{59}}}{{{88}}}}\)

Answer:

a) \(\displaystyle{\frac{{{6}}}{{{11}}}}\)

b) \(\displaystyle{\frac{{{5}}}{{{11}}}}\)

c) \(\displaystyle{\frac{{{59}}}{{{88}}}}\)