That event is dependent, because attaining a PhD can affect the probability of a person attaining a position as a professor. Most major universities require a Ph.D to become a professor.
As explained by Varsity Tutors, two events are independent if the result of the second event is not affected by the result of the first event.
On the other hand, two events are dependent if the result of the first event affects the outcome of the second event so that the probability is changed.
See Independent and Dependent Events examples at the following sites:
Shmoop
LearningWave