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Compute stockout sufficiency probability

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of discrete probability and binomial models for independent Bernoulli trials, testing the ability to compute the probability that a limited resource meets random demand.

  • easy
  • SIG (Susquehanna)
  • Statistics & Math
  • Data Scientist

Compute stockout sufficiency probability

Company: SIG (Susquehanna)

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Take-home Project

In a bakery, each customer buys one item: a croissant with probability 70% and a muffin with probability 30%, independently. There are 2 muffins left and 5 customers remain in line. What is the probability that the two muffins suffice (i.e., no customer wants a muffin after muffins are depleted)?

Quick Answer: This question evaluates understanding of discrete probability and binomial models for independent Bernoulli trials, testing the ability to compute the probability that a limited resource meets random demand.

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SIG (Susquehanna) logo
SIG (Susquehanna)
Aug 11, 2025, 12:00 AM
Data Scientist
Take-home Project
Statistics & Math
2
0

Probability That Muffins Suffice

Setup

  • Each of the 5 remaining customers independently chooses one item:
    • Croissant with probability 0.7
    • Muffin with probability 0.3
  • The bakery has 2 muffins left.

Task

What is the probability that the two muffins suffice for all remaining customers (i.e., there is no customer who wants a muffin after muffins are depleted)?

Hint: This is equivalent to “no more than 2 of the 5 customers want a muffin.”

Solution

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