Please help me understand our activity, I can't seem to understand the solution in the book.

1.If E is any event in sample space S show that E and S are Independent?

2.Three coins are tossed. Show that the event "heads on the first coin" and the event "tails on the two last coins" are independent.

3.In the two dice experiment

Given that r+w10, find the probability that r=5

Given that r+w=8, find the probability that w4.