A hat has nine coins in it. Four are fair, the other five have a chance...

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A hat has nine coins in it. Four are fair, the other five have a chance of heads on each toss (the tosses are independent). We choose a coin randomly and start flipping that same coin repeatedly. (a) If we get head and tail in the first two tosses, what is the probability we chose a fair coin? (b) If we get head and tail in the first two tosses, what is the probability the next flip will be heads? (c) Are the first and second flip of the coin that was chosen independent? Explain why or why not. (d) Suppose we flipped the same coin five times and have observed five heads. What's the probability that it was a fair coin? A hat has nine coins in it. Four are fair, the other five have a chance of heads on each toss (the tosses are independent). We choose a coin randomly and start flipping that same coin repeatedly. (a) If we get head and tail in the first two tosses, what is the probability we chose a fair coin? (b) If we get head and tail in the first two tosses, what is the probability the next flip will be heads? (c) Are the first and second flip of the coin that was chosen independent? Explain why or why not. (d) Suppose we flipped the same coin five times and have observed five heads. What's the probability that it was a fair coin?

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a If we get a head and a tail in the first two tosses the probability we chose a fair coin ... View the full answer