You have a fair five-sided dice. The sides of the dice are numbered from 1 to 5. Each dice roll is independent of all others, and all faces are equally likely to come out on top when the dice is rolled Suppose you roll the dice twice.

Part a

roll resulted in 5, and event C Let event A to be "the total of two rolls is 10", event B be "at least one be "at least one roll resulted in1" 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 o" Are events E and F independent? Are events E and F independent given event D?