Answer
$P(I~like~exactly~one~of~the~two~first~songs)=\frac{20}{39}\approx0.5128$
Work Step by Step
The events "I like the two first songs" and "I do not like the two first songs" are mutually exclusives (disjoint events).
Using the Addition Rule for Disjoint Events (page 270):
$P(I~like~the~two~first~songs~or~I~do~not~like~the~two~first~songs)=P(I~like~the~two~first~songs)+P(I~do~not~like~the~two~first~songs)=\frac{5}{39}+\frac{14}{39}=\frac{19}{39}$
The event "I like exactly one of the two first songs" is the complement of "I like the two first songs or I do not like the two first songs".
Using the Complement Rule (see page 275):
$P(I~like~exactly~one~of~the~two~first~songs)=1-P(I~like~the~two~first~songs~or~I~do~not~like~the~two~first~songs)=1-\frac{19}{39}=\frac{20}{39}\approx0.5128$
