In my opinion, Darrin's inference is wrong because according to given question, "Darrin surveyed a random sample of 10 students from his science class about their favorite types of TV shows."
This line provides the information that the survey is taken randomly. Also, if Darrin had taken some other students, then the ineference of other new students compared with previously surveyed students will be different.
This frankly tells that the probability is different always.
Therefore, Darrin's inference is wrong or invalid.