The Biased Coin Game

What this Bayesian inference interview question tests

This is a medium-difficulty probability question that combines prior distributions, likelihood, and posterior reasoning—core skills in quantitative trading and research. It asks you to update your belief about an unknown parameter given observed evidence, which is exactly how traders adjust models when new market data arrives.

To solve it, you need to apply Bayes' theorem: use the uniform prior on the coin bias, compute the likelihood of observing your specific sequence of flips under each possible bias value, and then find the posterior expectation. The problem rewards clear reasoning about conditional probability and comfort with integral calculus or a symmetry argument.

• Prior and posterior distributions
• Likelihood and Bayes' theorem
• Computing expected values under a posterior