Answer
The events are independent.
$P(Democrat~|~65+)=P(Democrat)$ and $P(65+~|~Democrat)=P(65+).$
Work Step by Step
The sample space: 4000 Iowa Voters. So, N(S) = 4000.
N(Democrat) = 1800, N(65+) = 1020 and N(Democrat and 65+) = 459. So:
$P(Democrat)=\frac{N(Democrat)}{N(S)}=\frac{1800}{4000}=0.45$. (Classical Method, page 259.)
$P(65+)=\frac{N(65+)}{N(S)}=\frac{1020}{4000}=0.255$. (Classical Method, page 259.)
Now:
$P(Democrat~|~65+)=\frac{N(Democrat~and~65+)}{N(65+)}=\frac{459}{1020}=0.45$ (Conditional Rule, page 288.)
$P(65+~|~Democrat)=\frac{N(Democrat~and~65+)}{N(Democrat)}=\frac{459}{1800}=0.255$ (Conditional Rule, page 288.)
$P(Democrat~|~65+)=P(Democrat)$ and $P(65+~|~Democrat)=P(65+).$
The events are independent. See definition, page 292.
