In order to find the answers for your question, consider the definition of the terms you're asking. The Independent variable is exactly that, independent. It's something that you can change. In this case, since the scientists are testing the drug XYZ, that doesnt change, what DOES change though are the AIDS patients Thus, the patients are your independent variable. The Dependent variable, is the variable that changes because of the independent variable. So if you changed patients what would you expect to change? In this case, you would except whether or not they develop fewer AIDS-realted illnesses to change right? So then their reaction to the drug would be your dependent variable. A Control Group is basically a way to test whether or not what you are changing in your experiment actually has an effect on its outcome. In this case (hypothetically...) patients who dont get this XYZ drug, what if these patients naturally develop fewer AIDS-related illnesses by themselves. We have no idea whether or not their reaction is due to the drug or because they would naturally have fewer illnesses. In this case, a control group could be a group of patients who do not receive the drug XYZ, or a placebo group. I know my explanation is probably a bit longer than what you were looking for, but I hope that in explaining it you'll be able to understand it and do future problems.