Probability- independent events

[C.E]

1. A fair coin is tossed n times, let E be the event that the first toss is a head and Fk be the event that there are a total of k heads. For which values of n, k are E and fk independent events?

3. I don't see how these events can possibly be independent (surely the first influences the second). Could somebody please explain how to do this question?

 

[Defennder]

You can approach this question mathematically instead of by conceptual reasoning. E and F_k are independent if P(E|F_k)=P(E) and P(F_k|E)=P(F_k).

Now you just have to find expressions for the above. Use Bayes theorem and the definition of conditional probability. After solving the above, you should be able to find n in terms of k.