Answer
They are not mutually exclusive.
Work Step by Step
The events “Republican” and “45-64” have outcomes in common.
Or:
$N(Republican~and~45-64) = 1075 \ne 0.$
Or:
$P(Republican~and~45-64) = \frac{N(Republican~and~45-64)}{N(S)}=\frac{1075}{4000}=0.26875\ne0.$
They are not mutually exclusive.
