Answer
$P(I~like~the~two~first~songs)=\frac{5}{39}\approx0.1282$
It is not an unusual event.
Work Step by Step
- Firt music:
The sample space are the 13 tracks. So, $N(S_1)=13$
I like 5 songs. Now, consider the event "I like the first song". $N(I~like~the~first~song)=5$
Using the Classical Method (page 259):
$P(I~like~the~first~song)=\frac{N(I~like~the~first~song)}{N(S_1)}=\frac{5}{13}$
- Second music:
The sample space are the 12 remaing tracks. So, $N(S_2)=12$
There are 4 songs that I like. Now, consider the event "I like the second song". $N(I~like~the~second~song~|~I~like~the~first~song)=4$
Using the Classical Method (page 259):
$P(I~like~the~second~song~|~I~like~the~first~song)=\frac{N(I~like~the~second~song~|~I~like~the~first~song)}{N(S_2)}=\frac{4}{12}=\frac{1}{3}$
Now, using the General Multiplication Rule (page 289):
$P(I~like~the~two~first~songs)=P(I~like~the~first~song)\times P(I~like~the~second~song~|~I~like~the~first~song)=\frac{5}{13}\times\frac{1}{3}=\frac{5}{39}\approx0.1282$
$P(I~like~the~two~first~songs)\gt0.05$. It is not an unusual event.
