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A friend claims that because there is a 50% chance for a coin to land on heads, the fact that the last three coin flips landed on tails means that there is a higher chance for the coin to land on heads with the next flip. Could you explain this problem with this reasoning?

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The coin has no memory and doesn't know what it did last time.

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  • $\begingroup$ It seems the question is more about whether the coin is actually fair. $\endgroup$
    – Alex R.
    Jun 5, 2016 at 19:36
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    $\begingroup$ @AlexR. If the coin was biased, then the next step should have a higher probability of tails, so the friend should be wrong in both cases :) $\endgroup$
    – jeff
    Jun 5, 2016 at 20:18
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If you treat the coin flips as independent, which is the usual assumption, then the previous flips have no effect on the next flip. So, this claim doesn't hold from this perspective.

However, a fair coin should have 50% heads if there are an infinite number of flips, so from this perspective, it seems reasonable to think that more heads will occur in the rest of the flips. But these three trials don't affect the rest of the trials, and 3 is too small as the number of trials anyway.

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