No tails are due

Understanding the gambler's fallacy in coin-flip expectations

This is a medium-difficulty probability question that tests whether you can reason clearly about independence and expected value in the face of a common cognitive bias. It's the kind of question quant firms use to check that a candidate doesn't conflate past outcomes with future probabilities.

The setup is deliberately provocative: after a streak of heads, intuition often whispers that a correction is "due." The question asks you to compute an expectation over a large sample of future flips, forcing you to think rigorously about what the history of a fair coin actually tells you about what comes next. Clean reasoning about independence and linearity of expectation will give you the answer.

• Independence of successive trials
• How memory (or the lack of it) affects probability
• Linearity of expectation over many trials