Medium · Probability & Combinatorics · Numerical · ~6 min · #48

Which Coin Did I Draw?

Real interview · Jane Street

A bag holds three coins that look identical. They land heads with probability $0.5$ , $0.6$ and $0.7$ respectively. You draw one coin at random, flip it, and it lands heads.

If you flip the same coin again, what is the probability it lands heads?

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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
Jane StreetGlassdoor interview question
Reported with biases 10%, 30% and 60% (answer 0.46).

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

Bayes' theoremPosterior predictive probability

Relevant for

Quant TraderQuant ResearcherDesk Quant