For all six points to lie within some interval of length 2, it is necessary and sufficient that:

February 22, 2026

For all six points to lie within some interval of length 2, it is necessary and sufficient that:

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Let each vehicle arrive at a time uniformly distributed over [0,10). We want the probability that there exists a 2-minute interval [t, t+2) ⊆ [0,10) such that all 6 arrival times fall within [t, t+2).
Standard technique: Compute the complementary probability — that **no** such interval covers all 6 points — and subtract from 1. However, due to complexity, we instead use geometric probability and order statistics.
Let $ X_1, X_2, \dots, X_6 \sim \text{Uniform}[0,10] $, and define $ X_{(1)} \leq X_{(2)} \leq \cdots \leq X_{(6)} $.
X_{(6)} - X_{(1)} \leq 2
Because then the earliest and latest arrivals are within 2 minutes, and the entire set fits in [X_{(1)}, X_{(1)} + 2].
Now, we compute:

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