[quenstionsasked]

This doesn't hold. The timing of the VPN code widget is not a random variable, but rather fixed. Thus, sampling a random inspection time of the widget has equal probability of being in the 0-30s bucket as it does in the 30-60s bucket.

For a bus, the intuitive explanation is that if you were viewing a timeline, the biggest parts of the timeline would be the "late" buses, and thus you're more likely to "inspect" (arrive at the bus stop) during one of these longer stretches.