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Consecutive Tails in Coin Flips

Imagine flipping a fair coin 10 times. What is the probability that you end up with exactly three tails, with all tails appearing consecutively? For instance, a sequence like HHHHTTTHHH would satisfy this condition. Bonus: How would you calculate the probability of obtaining exactly t tails in n coin flips (where t ≤ n), with all tails occurring consecutively?

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Consecutive Tails in Coin Flips

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Consecutive Tails in Coin Flips

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