For non-mutually exclusive events, the probability can be calculated using the formula
[tex]P(A\text{ or B) = P(A) + P(B) - P(A }\cap B)[/tex]Let's take
A = Faculty Member
B = Female
The probability of A will be
[tex]P(A)=\frac{80}{880}[/tex]The probability of B will be
[tex]P(B)=\frac{330}{880}[/tex]The probability of (A n B), that is, the number of faculty members that are females, will be
[tex]P(A\cap B)=\frac{30}{880}[/tex]Therefore, the probability will be calculated as
[tex]\begin{gathered} P(\text{A or B) }=\text{ }\frac{80}{880}+\frac{330}{880}-\frac{30}{880} \\ =\frac{380}{880} \\ =0.432 \end{gathered}[/tex]The probability is 0.43.
