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Mystery of the Biased Coin
You have a coin that may or may not be biased. After flipping it 10 times, you observe 7 heads and 3 tails.
1. What is the probability that the coin is biased, given that the prior belief is 50% for the coin being fair or biased?
2. Assume that if the coin is biased, the probability of heads is 0.8. How would Bayes' Theorem be applied to determine the posterior probability of bias?
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