Coin probability problem

Question

A coin with probability p of heads is tossed n times. Let E be the event ‘a head is obtained on the first toss’ and F_k the event ‘exactly k heads are obtained’. For which pairs of integers (n, k) are E and F_k independent? 

Answer 1

They are dependent only when n=1 because, if E occurs then so does F_k, (k=1) and if E doesn't occur, then neither does F_k (k=0).

When n>1, E may or may not occur. If E occurs, F_k also occurs (1≤k≤n); but if E does not occur, F_k may occur (1≤k≤n-1). So F_k is independent of E. Also E is independent of F_k.