Calculate Probability and Statistics for Dice Roll Outcomes

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Calculate Probability and Statistics for Dice Roll Outcomes states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate Probability and Statistics for Dice Roll Outcomes

Company: Boston Consulting Group

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Take-home Project

##### Scenario A casino analyst models dice rolls to understand outcome probabilities for marketing promotions. ##### Question You roll a fair six-sided die 10 times. What is the probability of observing exactly 3 sixes? What is the expected number and standard deviation of sixes in those 10 rolls? ##### Hints Use the Binomial distribution: n = 10, p = 1/6.

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 Calculate Probability and Statistics for Dice Roll Outcomes states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Calculate Probability and Statistics for Dice Roll Outcomes

Dice Rolls and the Binomial Model

Scenario

A casino analyst models dice rolls to understand outcome probabilities for marketing promotions.

Question

You roll a fair six-sided die 10 times. Let X be the number of sixes observed.

Compute:

  1. P(X = 3) — the probability of observing exactly 3 sixes.
  2. E[X] — the expected number of sixes in 10 rolls.
  3. SD[X] — the standard deviation of the number of sixes.

Hint: Model X with a Binomial distribution: n = 10, p = 1/6.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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