(a) Suppose that we flip three coins. If all of them show heads, we stop. If...

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(a) Suppose that we flip three coins. If all of them show heads, we stop. If at least one tail comes up, we flip all three coins again. What is the probability that we repeat this experiment n times? (b) Suppose that we roll a fair die. If in the first roll a 1 comes up, we stop. Otherwise we keep going. If in the second roll a 2 comes up, we stop. Otherwise we keep going, etc. What is the probability that we never stop rolling the die? (a) Suppose that we flip three coins. If all of them show heads, we stop. If at least one tail comes up, we flip all three coins again. What is the probability that we repeat this experiment n times? (b) Suppose that we roll a fair die. If in the first roll a 1 comes up, we stop. Otherwise we keep going. If in the second roll a 2 comes up, we stop. Otherwise we keep going, etc. What is the probability that we never stop rolling the die?