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This question is commonly asked for Data Scientist candidates at Boston Consulting Group during technical interviews.

Calculate Probability and Statistics for Dice Roll Outcomes

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of discrete probability and the Binomial distribution, specifically computing point probabilities, expected value, and standard deviation for count data.

Boston Consulting Group

Aug 4, 2025, 10:55 AM

Data Scientist

Take-home Project

Statistics & Math

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:

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

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

Solution

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