Compute posterior and predictive coin probabilities
Company: Boston Consulting Group
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
You have two coins: F is fair; B is biased with P(H)=0.7. You pick one coin uniformly at random and flip it three times. The first two flips are Heads (the third flip outcome is not yet observed). a) Compute P(picked B | first two flips are Heads). b) Compute P(next flip is Heads | first two flips are Heads). c) Continuing with the same coin, let T be the total number of flips until the first Tail occurs (including it). Compute E[T | first two flips are Heads], showing your derivation.
Quick Answer: This question evaluates Bayesian inference and probabilistic reasoning, focusing on posterior updating, posterior predictive probability, and the conditional expectation of a stopping time given observed outcomes.