Easy · Probability & Combinatorics · Multiple choice · ~4 min · #100

One Fair Coin Among Many

Real interview · Jane Street, Millennium

You flip 100 coins with arbitrary biases, at least one of which is fair and at least one of which is not. Is the probability of an even number of heads sometimes $\tfrac12$ , always $\tfrac12$ , or never $\tfrac12$ ?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

Jane StreetGlassdoor interview question
Millennium· Quant Research InternGlassdoor interview reviews
Reported as finding a necessary and sufficient condition on the biases.

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Conditioning on the last stepParity

Relevant for

Quant ResearcherQuant Trader