Compute stockout sufficiency probability
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.
SIG (Susquehanna)
Aug 11, 2025, 12:00 AM
Data Scientist
Take-home Project
Statistics & Math
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Probability That Muffins Suffice
Setup
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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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