For #8:  The Hint is Spot-on.  Remember:

Probability of surviving in spot A_n = n/10 * probability of surviving in spot A_n-1 +

                                                                            (10-n)/10 * probability of surviving in spot A_n+1

And A_5. Hmmm.... It's not leaned in one way or another.

For #9: Casework with number of heads!

For #10: Geometric sequences can be written as a, ar, ar^2, ar^3, ar^4....ar^29.  How can you choose 3 of these such that they are in a geometric sequence.  (This is casework with ratio)

Hope these helped! Might have given away too much.