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. 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? $(10$ points$)-$ Are events E and F independent given event D$?(10$ points$)$