Final answer:
Going to the gym and losing weight are not independent events as the occurrence of one can influence the likelihood of the other; however, they're not mutually exclusive since weight loss can occur without gym attendance and vice versa.
Step-by-step explanation:
The answer to whether going to the gym and losing weight are independent events is B. No, and they are not mutually exclusive either. Independence in events means that the occurrence of one event does not influence the probability of the other event occurring. In this context, going to the gym is an activity that can contribute to weight loss by increasing calorie expenditure. Thus, the two events are related because going to the gym can increase the likelihood of weight loss. However, they are not mutually exclusive because one can lose weight without going to the gym, through diet or other activities, and one can go to the gym without losing weight, perhaps by focusing on strength training or consuming enough calories to maintain or even gain weight.