Compute odds under time pressure

Q: Compute odds under time pressure

This is a Statistics & Math interview question from Optiver for Data Scientist roles. View the full question and solution on PracHub.

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Question

Timed Probability: At Least Two Reds in Three Draws

You have an urn with r red, b blue, and g green balls. Let N = r + b + g with r, b, g ≥ 0 and N ≥ 3. You draw 3 balls.

Tasks:

Baseline (without replacement): Compute P(at least two reds).
Fast mental-math method that scales to general r, b, g.
Extensions: (i) Drawing with replacement. (ii) Conditional probability given that the first ball drawn was green. (iii) Express the answer in odds form, suitable for quick estimation.

Compute odds under time pressure

Timed Probability: At Least Two Reds in Three Draws

Solution (Locked)

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