# From the same data, answer the following - What is the probability

From the same data, answer the following
- What is the probability that it is a male or in managerial position?
- What is the probability that it is neither male nor in managerial position
- What is the probability that it is female or clerical portion?
$\begin{array}{|c|c|} \hline Position&Male&Female&Total\\ \hline Managerial&8&4&12\\ \hline Engineer&18&7&25\\ \hline Accountant&3&5&8\\ \hline Clerical&15&28&43\\ \hline Total&44&44&88\\ \hline \end{array}$

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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)
$$\displaystyle={\frac{{{n}{\left(\text{female or clerical portion}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}$$
$$\displaystyle={\frac{{{n}{\left({f}{e}{m}{a}le\right)}+{n}{\left(\text{clerical portion}\right)}-{n}{\left(\text{female and clerical portion}\right)}}}{{{n}{\left(to{t}{a}{l}\right)}}}}$$
$$\displaystyle={\frac{{{44}+{43}-{28}}}{{{88}}}}$$
$$\displaystyle={\frac{{{59}}}{{{88}}}}$$
a) $$\displaystyle{\frac{{{6}}}{{{11}}}}$$
b) $$\displaystyle{\frac{{{5}}}{{{11}}}}$$
c) $$\displaystyle{\frac{{{59}}}{{{88}}}}$$