Bathroom occupancy — discrete-event Monte-Carlo

The house, one sampled run

Day 1 · 00:00 occupied: 0 / 2 speed 2×

vacant bathroom occupied turned away (both busy)

Each person heads to a bathroom 3× a day at random times, 20 min each. If both bathrooms are busy, the arrival is rejected — no one shares a stall, no one waits. The playhead below scrubs the sampled timeline.

How often is a bathroom in use?

No bathroom

–

both free

One bathroom

–

exactly one busy

Both bathrooms

–

house at capacity

Monte-Carlo (simulated) binomial (theory)

Simulated vs. closed-form theory

Quantity	Simulated	Binomial

🚻 Bathroom occupancy — a discrete-event Monte-Carlo

The house, one sampled run

How often is a bathroom in use?

Simulated vs. closed-form theory

Monte-Carlo convergence