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Compute probability match lasts 5 games

WaymoData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question evaluates understanding of discrete probability, sequential best-of-n match modeling, Monte Carlo simulation for probability estimation, and interval estimation for proportions.

Two players play independent games of table tennis.

  • Player A wins each game with probability (p) (constant across games).
  • They play a best-of-5 match (first to 3 wins).
  • Let (X) be the number of games played until the match ends (so (X\in{3,4,5})).

Tasks

  1. Compute (\theta = \Pr(X=5)).
  2. Write a simulation (Monte Carlo) approach to estimate (\theta).
  3. Follow-up: given (M) simulated matches, how would you build a confidence interval for (\theta)?