Find probability of overlapping blooms

Q: Find probability of overlapping blooms

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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Question

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)?

Find probability of overlapping blooms

Overlap Probability of Two Random Bloom Periods

Solution

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Find probability of overlapping blooms

Overview

Overlap Probability of Two Random Bloom Periods

Solution

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