Answer
The percentage of new hires which will be minority females is 15%.
Work Step by Step
Let $A$ be the event that the new employees will be female and let $B$ be the event that the new employees will be minorities. Then
\[\begin{align}
& P(A)=0.60 \\
& P(B)=0.30 \\
\end{align}\]
And let \[{{A}^{C}}\] be the event that the new employees will be male and let ${{B}^{C}}$ be the event that the new employees will be white.
Since one out of four new employees will be a white male, that means
\[P({{A}^{C}}\cap {{B}^{C}})=\frac{1}{4}=0.25\]
By DeMorgan’s theorem,
\[\begin{align}
& P({{A}^{C}}\cap {{B}^{C}})=1-P(A\cup B) \\
& P(A\cup B)=1-P({{A}^{C}}\cap {{B}^{C}}) \\
& P(A\cup B)=1-0.25 \\
& P(A\cup B)=0.75 \\
\end{align}\]
Therefore \[P({{A}^{C}}\cap {{B}^{C}})\] becomes
\[\begin{align}
& P(A\cap B)=P(A)+P(B)-P(A\cup B) \\
& P(A\cap B)=0.60+0.30-0.75 \\
& P(A\cap B)=0.15 \\
\end{align}\]
