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The probability of getting a head first time is one out of two, or a half.

The probability of getting a head the next time is still one out of two, so the combined probability is one quarter. Similarly, one eighth is the probability of getting three in a row; but the pattern does not end there, the probability of getting a tails the next time is STILL one in two, so that is a one in sixteen chance of that run, the probability of the entire sequence is therefore one in thirty-two.

The probability of getting a head the next time is still one out of two, so the combined probability is one quarter. Similarly, one eighth is the probability of getting three in a row; but the pattern does not end there, the probability of getting a tails the next time is STILL one in two, so that is a one in sixteen chance of that run, the probability of the entire sequence is therefore one in thirty-two.

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Q: What is the probability of getting a run of three consecutive heads before a run of two consecutive tails when tossing a fair coin over and over?

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