Peeking at a Fair Coin
A fair coin is flipped 10 times. After each flip the experimenter checks the running difference D = (heads) - (tails), and declares the coin "biased towards heads" the first moment D reaches +4 (and then stops). What is the exact probability, for a truly fair coin, that the experimenter ever declares it biased within the 10 flips? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Peeking Problem 4.0/10
Source: Discrete optional-stopping illustration via the reflection principle. Statement written for AxiomIQ.