Find the Probability Two Muffins Are Sufficient
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Find the Probability Two Muffins Are Sufficient
Each of five customers independently buys exactly one item. A customer chooses a croissant with probability 75% and a muffin with probability 25%. The bakery has two muffins remaining.
What is the probability that no customer who wants a muffin finds the muffins sold out? Express the answer as a percentage rounded to the nearest whole percent using half-up rounding.
### What a Strong Answer Covers
- Translation of “sufficient” into at most two muffin requests.
- A binomial calculation for zero, one, or two muffin buyers.
- Correct use of five independent trials and a 25% muffin probability.
- Conversion and rounding of the final probability.
### Follow-up Questions
- How many muffins are needed to make the sufficiency probability at least 99%?
- How would dependence between customers' choices affect the calculation?
Overview: Model five independent bakery choices with a binomial random variable and ask whether two muffins cover demand. The solution sums the zero-, one-, and two-request cases, obtains 459/512, and rounds the resulting 89.648% probability to 90%.
Read the full Sig Data Scientist interview experience this question came from