Total number of physicians: 510
Number of female physicians: 85
Number of dermatologists: 42
Number of female dermatologists: 14
P(female) = 85/510 = 1/6 = 0.167
P(female\dermatologist) = 14/42 = 1/3 = 0.333
Since P(female\dermatologist) is diferent from P(female), 'Female' and 'Dermatologist' are dependent events.
Since there is dermatologists that are females, the events 'Female' and "Dermatologist' are mutually non-exclusive