Answer
$P(first~is~Yolanda~and~second~is~Lorrie)=\frac{1}{20}=0.05$
Work Step by Step
- First home:
The sample space = {Yolanda, Lorrie, Laura, Kim, Anne Marie}. So, $N(S_1)=5$
Now, consider the event "first is Yolanda". $N(first~is~Yolanda)=1$
Using the Classical Method (page 259):
$P(first~is~Yolanda)=\frac{N(first~is~Yolanda)}{N(S_1)}=\frac{1}{5}$
- Second home:
The sample space = {Lorrie, Laura, Kim, Anne Marie}. So, $N(S_2)=4$
Now, consider the event "second is Lorrie". $N(second~is~Lorrie~|~first~is~Yolanda)=1$
Using the Classical Method (page 259):
$P(second~is~Lorrie~|~first~is~Yolanda)=\frac{N(second~is~Lorrie~|~first~is~Yolanda)}{N(S_2)}=\frac{1}{4}$
Now, using the General Multiplication Rule (page 289):
$P(first~is~Yolanda~and~second~is~Lorrie)=P(first~is~Yolanda)\times P(second~is~Lorrie~|~first~is~Yolanda)=\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}=0.05$