Find probability of overlapping blooms

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.

Find probability of overlapping blooms

Company: SIG (Susquehanna)

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Online Assessment

Two flowers bloom independently. The purple flower’s blossom time is uniformly random over the next 30 days and lasts exactly 9 days. The red flower’s blossom time is uniformly random over the next 30 days and lasts exactly 12 days. What is the probability that the two flowers overlap in bloom at some point?

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.

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SIG (Susquehanna)
Aug 11, 2025
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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)?
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