Answer:
No, the events are not independent.
Explanation:
Suppose that there are two events, A and B.
Such that first happens the event A and then the event B.
If the outcome of event A affects the probabilities for the different outcomes of event B, then the events are dependent.
In this case, if we have only the event "selecting a student who has brown eyes" (at random)
The probability is equal to the quotient between the total number of students with brown eyes, and the total number of students, then this probability is:
P = 91/200 = 0.455...
Now, if we first impose the "selecting a female", now when we want to select a student with brown eyes we will look only at the female students.
In this case, there are 32 with brown eyes and a total of 90 female students, then the probability of selecting a female with brown eyes at random is:
P = 32/90 = 0.355...
So the probability is different, which means that the events "selecting a female" and "selecting a student who has brown eyes" are not independent.