← Boston Consulting Group Interview Insights

Boston Consulting Group·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

Interviewed for a Data Scientist role at BCG and got hit with a probability question that felt more like a stats exam than a job interview. Not a bad experience, just a bit academic.

Questions Asked (1)

Q1

You roll a fair six-sided die 10 times. What is the probability of getting exactly 3 sixes? Also, what are the expected number and standard deviation of sixes across those 10 rolls?

Product Analytics & MetricsAlgorithms & Data Structures
Author's notes

I knew it was binomial the second they said 'exactly 3' but I fumbled the standard deviation formula for a moment.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Recognize this as a binomial distribution problem with n=10 and p=1/6. Calculate the probability of exactly 3 sixes using the binomial formula, then compute the expected value and standard deviation using the binomial formulas. Clearly state assumptions and interpret results in context.

Pro tip: After computing the numbers, briefly explain what they mean in a business context—e.g., how likely it is to observe 3 sixes and how much variation to expect—to demonstrate practical insight.

1. Identify the distribution

State that the number of sixes in 10 independent rolls follows a binomial distribution with parameters n=10 and p=1/6.

2. Calculate probability of exactly 3 sixes

Use the binomial probability formula: P(X=3) = C(10,3) * (1/6)^3 * (5/6)^7. Compute the combination and powers to get the numerical value.

3. Compute expected number of sixes

Use the binomial mean formula: E[X] = n * p = 10 * (1/6) = 10/6 ≈ 1.6667.

4. Compute standard deviation

Use the binomial variance formula: Var(X) = n * p * (1-p) = 10 * (1/6) * (5/6) = 50/36 ≈ 1.3889. Then take the square root to get the standard deviation: √(50/36) ≈ 1.1785.

5. Interpret and summarize

Present the final answers: probability ≈ 0.155, expected value ≈ 1.67, standard deviation ≈ 1.18. Briefly interpret these results in the context of the problem.

Key Points to Mention

  • Binomial distribution assumptions: fixed number of trials, independent trials, constant probability of success, two outcomes.
  • Binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k).
  • Combination calculation: C(10,3) = 120.
  • Expected value formula for binomial: E[X] = n * p.
  • Variance formula for binomial: Var(X) = n * p * (1-p).
  • Standard deviation is the square root of variance.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.