Does it make a difference if the coin is fair or unfair how, Econometrics

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Does it make a difference if the coin is fair or unfair how

A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is a head. Is she right? Does it make a difference if the coin is fair or unfair? How can we generalize Alice reasoning?

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