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Math Help - independent events

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    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?

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    Quote Originally Posted by nmatthies1 View Post
    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)?
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