Answer
$P(first~is~Roger~and~second~is~Rick)=\frac{1}{42,165,542}\approx0.00000002372$
Work Step by Step
- First resident:
The sample space: 6494 people. So, $N(S_1)=6494$
Consider the event "first resident is Roger Cummings". $N(first~resident~is~Roger)=1$
Using the Classical Method (page 259):
$P(first~resident~is~Roger)=\frac{N(first~resident~is~Roger)}{N(S_1)}=\frac{1}{6494}$
- Second resident:
The sample space: 6493 remaining people. So, $N(S_2)=6493$
Consider the event "second resident is Rick Whittingham". $N(second~resident~is~Rick~|~first~resident~is~Roger)=1$
Using the Classical Method (page 259):
$P(second~resident~is~Rick~|~first~resident~is~Roger)=\frac{N(second~resident~is~Rick~|~first~resident~is~Roger)}{N(S_2)}=\frac{1}{6493}$
Now, using the General Multiplication Rule (page 289):
$P(first~is~Roger~and~second~is~Rick)=P(first~resident~is~Roger)\times P(second~resident~is~Rick~|~first~resident~is~Roger)=\frac{1}{6494}\times\frac{1}{6493}=\frac{1}{42,165,542}\approx0.00000002372$
