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Compute probability in urn with green returns

Virtu FinancialData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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Compute probability in urn with green returns evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

An urn contains 5 red, 5 blue, and 5 green balls. You repeatedly draw one ball uniformly at random. If the ball is green, immediately return it to the urn and continue; if it is red or blue, keep it. Stop once you are holding three balls (i.e., three non-green balls).

  1. What is the probability that at least two of the three held balls are red?
  2. Now suppose the urn instead has 10 red, 5 blue, and 5 green balls (same process). First give an intuitive estimate, then compute the exact probability that at least two of the three held balls are red.