You have a fair five-sided dice. The sides of the dice are numbered from 1 to 5 . Suppose you roll the dice twice (independently). Answer the following questions and explain your solution for each part. Part a Let event A to be the total of two rolls is 10 , event B be at least one roll resulted in 5 , and event C be at least one roll resulted in 1 . Is event A independent of event B? Is event A independent of event C? Part b Let event D be the total of two rolls is 7, event E be the difference between the two roll outcomes is exactly 1, and event F be the second roll resulted in a higher number than the first roll. Are events E and F independent? Are events E and F independent given event D ?