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Double-Sided Coin Probability

HardStatistics & Probability00:00
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Your question is Double-Sided Coin Probability. Take a moment with it on the right.

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Problem

You have a bag of coins where one coin is double-sided (heads on both sides) and the rest are fair. You pick a coin at random and flip it three times; it lands on heads each time. What is the probability that you chose the double-sided coin?