The best answer for these question would be:
A. Flipping two coins and having one show a head and the other show a head
D. Rolling a 4 on one die and rolling a 2 on another die
E. Seeing clouds and winning the lottery
Independent events in math means that the first situation does not affect the other variable. It is generally the individual probability that will happen to the solution. Which means that you have to determine whether the first situation will be affected on the second events that will happen. While the dependent events, have the opposite effect.