Answer
$P(first~is~Roger~and~second~is~Rick)=\frac{1}{42,172,036}=0.00000002371$
The result, assuming independence, ($0.00000002371$) is very close to the exact result ($0.00000002372$)
Work Step by Step
Assuming independence:
$P(first~resident~is~Roger)=P(second~resident~is~Rick)=\frac{1}{6494}$
Using the Multiplication Rule for Independent Events (page 282):
$P(first~is~Roger~and~second~is~Rick)=P(first~resident~is~Roger)\times P(second~resident~is~Rick)=\frac{1}{6494}\times\frac{1}{6494}=\frac{1}{42,172,036}=0.00000002371$
The result, assuming independence, ($0.00000002371$) is very close to the exact result ($0.00000002372$)
