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SIG (Susquehanna)·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

SIG probability question for a Data Scientist role. One problem, no fluff, just math under pressure.

Questions Asked (1)

Q1

A bakery has 2 muffins left and 5 customers still in line. Each customer independently buys a muffin with 30% probability and a croissant with 70%. What is the probability that the muffins don't run out before everyone is served?

Algorithms & Data StructuresProduct Analytics & Metrics
Author's notes

This one took me longer than it should have.

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Suggested Approach

Model the number of muffin buyers among the 5 customers as a Binomial(5, 0.3) random variable. The muffins run out if 3 or more customers buy muffins, so compute the probability that at most 2 customers buy muffins using the binomial PMF or CDF.

Pro tip: Clearly state that each customer's choice is independent and that the probability of buying a muffin is constant at 0.3. This shows you understand the assumptions behind the binomial model and avoids ambiguity.

1. Define the random variable

Let X be the number of customers who buy a muffin. X follows a Binomial distribution with n = 5 trials and success probability p = 0.3.

2. Identify the condition for muffins not running out

There are 2 muffins available, so they do not run out if X ≤ 2. We need to find P(X ≤ 2).

3. Compute the probability using the binomial formula

Calculate P(X = 0), P(X = 1), and P(X = 2) using the binomial PMF: P(X = k) = C(5, k) * (0.3)^k * (0.7)^(5-k). Sum these probabilities.

4. Perform the arithmetic

Compute each term: P(X=0) = 0.7^5 = 0.16807, P(X=1) = 5 * 0.3 * 0.7^4 = 0.36015, P(X=2) = 10 * 0.3^2 * 0.7^3 = 0.3087. Sum = 0.83692.

5. State the final probability

The probability that the muffins don't run out is approximately 0.8369 or 83.69%.

Key Points to Mention

  • Binomial distribution assumptions: independent trials, constant probability of success.
  • Definition of success: a customer buys a muffin (p = 0.3).
  • Complementary event: muffins run out if X ≥ 3, so P(not run out) = 1 - P(X ≥ 3).
  • Calculation of binomial coefficients and powers.
  • Interpretation of the result in the context of the problem.
  • Potential alternative approach: simulate or use normal approximation (though not necessary here).

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