Answer
$P(I~do~not~like~the~two~first~songs)=\frac{14}{39}\approx0.3590$
Work Step by Step
- First music:
The sample space are the 13 tracks. So, $N(S_1)=13$
I do not like $13-5=8$ songs. Now, consider the event "I do not like the first song". $N(I~do~not~like~the~first~song)=8$
Using the Classical Method (page 259):
$P(I~do~not~like~the~first~song)=\frac{N(I~do~not~like~the~first~song)}{N(S_1)}=\frac{8}{13}$
- Second music:
The sample space are the 12 remaing tracks. So, $N(S_2)=12$
There are 7 songs that I do not like. Now, consider the event "I do not like the second song". $N(I~do~not~like~the~second~song~|~I~do~not~like~the~first~song)=7$
Using the Classical Method (page 259):
$P(I~do~not~like~the~second~song~|~I~do~not~like~the~first~song)=\frac{N(I~do~not~like~the~second~song~|~I~do~not~like~the~first~song)}{N(S_2)}=\frac{7}{12}$
Now, using the General Multiplication Rule (page 289):
$P(I~do~not~like~the~two~first~songs)=P(I~do~not~like~the~first~song)\times P(I~do~not~like~the~second~song~|~I~do~not~like~the~first~song)=\frac{8}{13}\times\frac{7}{12}=\frac{56}{156}=\frac{14}{39}\approx0.3590$
