A coin has been flipped 5 times in a row, landing heads every time
A coin has been flipped 5 times in a row, landing heads every time. Sameer thinks it is "due" for tails now, so the next flip is more likely to be tails than heads. His sister says both are still equally likely. Who is right?
Who do you think is right? Pick one.
The answer: His sister is right, every flip is independent — the odds are still equal
Why
Sameer's idea — that a fair coin somehow 'remembers' its past results and rebalances itself — feels natural, since 5 heads in a row does look unusual. But a coin has no memory at all; it does not know or care what happened on the previous flip, and each flip is a completely fresh, independent event with the exact same 50-50 odds as every other flip, no matter what came before. The unusual thing was seeing 5 heads in a row in the FIRST place (a genuinely rare sequence, about a 1-in-32 chance) — but once that has already happened, the 6th flip is just an ordinary new flip, unconnected to the streak behind it. Test it: imagine a brand-new coin, never flipped before — it also has exactly a 50-50 chance of landing heads. The already-flipped coin, at the moment of its 6th flip, is in the identical position as that brand-new coin — the past flips changed nothing about how the coin will land next. His sister is right: each flip stays a 50-50 chance regardless of the streak before it — this mistaken idea that a random event is 'due' to balance out is well known enough to have its own name, the gambler's fallacy.
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