Answer
$P(I~will~accept)=0.8$
Work Step by Step
- First DVD:
The sample space are the 10 DVD players. So, $N(S_1)=0$
9 DVD players work. Now, consider the event "first DVD works". $N(first~DVD~works)=9$
Using the Classical Method (page 259):
$P(first~DVD~works)=\frac{N(first~DVD~works)}{N(S_1)}=\frac{9}{10}$
- Second DVD:
The sample space are the 9 remaining DVD players. So, $N(S_2)=9$
Now, 8 DVD players work. Now, consider the event "second DVD works". $N(second~DVD~works~|~first~DVD~works)=8$
Using the Classical Method (page 259):
$P(second~DVD~works~|~first~DVD~works)=\frac{N(second~DVD~works~|~first~DVD~works)}{N(S_2)}=\frac{8}{9}$
Now, using the General Multiplication Rule (page 289):
$P(I~will~accept)=P(both~DVD~work)=P(first~DVD~works)\times P(second~DVD~works~|~first~DVD~works)=\frac{9}{10}\times\frac{8}{9}=\frac{8}{10}=0.8$
