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Find expected tosses to see a coin pattern

BnpData Scientist · Technical Screen
EasyData ScientistTechnical ScreenSoftware Engineering Fundamentals

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Assesses probabilistic reasoning and stochastic-process modeling skills, focusing on expected stopping times for pattern occurrences in repeated independent trials and related concepts like state-space representation and overlap effects.

A fair coin is tossed repeatedly until a target length-3 pattern appears as a consecutive substring (e.g., HHH, HTH, HTT, etc.).

  1. Describe a general method to compute the expected number of tosses to see a given pattern.
  2. Compute the expected number of tosses for HHH and for HTH.