Probability Bayes theorem

You are given a coin which you know is either fair or double-headed. You believe that the a priori odds of it being fair are F to 1; i.e., you believe that the a priori probability of the coin being fair is F F +1 . You now begin to flip the coin in order to learn more. Obviously, if you ever see a tail, you know immediately that the coin is fair. As a function of F, how many heads in a row would you need to see before becoming convinced that there is a better than even chance that the coin is double-headed? 

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