Answer
$P(first~person~is~Dave~and~second~person~is~Neta)=\frac{1}{20}=0.05$
Work Step by Step
We are assuming that the sampling is done without replacement, that is, the second person chosen must be different from the first person chosen.
- First person chosen:
The sample space = {Mike, Neta, Jinita, Kristin, Dave}. So, $N(S_1)=5$
Now, consider the event "first person is Dave". $N(first~person~is~Dave)=1$
Using the Classical Method (page 259):
$P(first~person~is~Dave)=\frac{N(first~person~is~Dave)}{N(S_1)}=\frac{1}{5}$
- Second person chosen:
The sample space = {Mike, Neta, Jinita, Kristin}. So, $N(S_2)=4$
Now, consider the event "second person is Neta". $N(second~person~is~Neta~|~first~person~is~Dave)=1$
Using the Classical Method (page 259):
$P(second~person~is~Neta~|~first~person~is~Dave)=\frac{N(second~person~is~Neta)}{N(S_2)}=\frac{1}{4}$
Now, using the General Multiplication Rule (page 289):
$P(first~person~is~Dave~and~second~person~is~Neta)=P(first~person~is~Dave)\times P(second~person~is~Neta~|~first~person~is~Dave)=\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}=0.05$
