Derive Probability of Even Sum in Bernoulli Trials
Company: Boston Consulting Group
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
##### Scenario
Online assessment requires candidates to solve non-formulaic probability puzzles within strict proctoring constraints.
##### Question
Let X1,…,Xn be i.i.d. Bernoulli(p). Derive a closed-form expression for P(Σ_i X_i is even). A fair coin is flipped until two consecutive identical outcomes appear. What is the expected number of flips?
##### Hints
Use moment-generating tricks or parity arguments for the first; write a recurrence or Markov chain for the second.
Quick Answer: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Derive Probability of Even Sum in Bernoulli Trials states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.