Probability of a coin being fair from an unkown sample

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Suppose you have a bag of n coins. There a k unknown biased coins in the bag and the rest are fair coins, with k in the range [0,n].

Is it possible to measure the probability that a randomly sampled coin c is an unfair coin (without knowing k; the total number of biased coins)? Or additionally are there any methods wan reveal any insights this problem?

My intuition is that it's impossible...