# Math Help - independent events

1. ## independent events

A fair coin is tossed n times. Let E be the event that the first toss is a head, and let $F_k$ be the event that there are k heads in total. For what values of n, k are E and $F_k$ independent?

What do I use here?

2. Originally Posted by nmatthies1
A fair coin is tossed n times. Let E be the event that the first toss is a head, and let $F_k$ be the event that there are k heads in total. For what values of n, k are E and $F_k$ independent?
Is it clear to you that $P(E) = 0.5$?
If $0 < k \leqslant n$, is it true that $P\left( {F_k } \right) = {\binom{n}{k}}\left( {0.5} \right)^n$?

$0 < k < n$ then $P\left( {E \cap F_k } \right) = P\left( {F_k |E} \right)P(E) = {\binom{n-1}{k-1}}\left( {0.5} \right)^n$.

Can you find the values such that $P\left( E \right) \cdot P\left( {F_k } \right) = P\left( {E \cap F_k } \right)$?