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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

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This is a medium difficulty Statistics & Math question, commonly asked during Take-home Project rounds at SIG (Susquehanna).

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This question is commonly asked for Data Scientist candidates at SIG (Susquehanna) during technical interviews.

Find probability of overlapping blooms

Last updated: Jun 12, 2026

Quick Overview

This question evaluates understanding of probability theory, specifically reasoning about continuous uniform distributions, geometric probability, and the likelihood of overlap between random time intervals within a fixed horizon.

SIG (Susquehanna)

Aug 11, 2025, 12:00 AM

Data Scientist

Take-home Project

Statistics & Math

Overlap Probability of Two Random Bloom Periods

Assumptions

Time is measured in days over a 30-day horizon.
Each flower begins blooming once, at a start time chosen independently and uniformly at random in [0, 30].
Purple bloom length: 9 days. Red bloom length: 12 days.

Question

What is the probability that the two flowers overlap in bloom at some point (i.e., there is at least one day when both are simultaneously in bloom)?

Solution

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