Will two flowers bloom?

What this geometric-probability interview question tests

This is a hard probability question that combines uniform random variables with interval overlap — a classical setup in quant interviews. It rewards the ability to translate a real-world scenario into a precise mathematical model and then compute the probability of a joint event without getting lost in casework.

The core challenge is recognizing that you're working with two independent start times, each uniform over a fixed window, and that the "two flowers bloom simultaneously" condition depends on whether their individual bloom intervals overlap in time. Strong solutions typically visualize the problem in the space of possible outcomes, identify the region where the condition holds, and compute its measure relative to the total space. This approach avoids tedious case analysis and generalizes to similar problems.

• Geometric probability in two dimensions
• Independence and joint distributions of uniform random variables
• Interval overlap conditions
• Symmetry and measure over a constrained region