Which of the following probabilities are most likely independent? a. the chance a student will study for his test and the chance he will get an a b. the chance a student practices foul shots regularly and the chance he will make the basketball team c. the chance a student has blue eyes and the chance the student is a girl d. the chance a woman exercises and the chance that she works from home

A. The chance a student will study for his test and the chance he will get an A.
The two events are dependent, because the chance a student will get an A depends on the fact if he will study or not.
 B. The chance a student practices foul shots regularly and the chance he will make the basketball team
The events are also dependent. If the student practices full shot he will have a bigger chance to get in the basketball team.
C. The chance a student has blue eyes and the chance the student is a girl. These are independent events.
 D. The chance a woman exercises and the chance that she works from home . These are also independent events and have no influence of each other.

Both C and D (assuming this is multiple choice). Having blue eyes doesn't cause you to be a girl and exercising doesn't cause you to work at home, those variables aren't dependent. 

Source: APEX and my brain lol

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