The late bus

Every morning I leave home at 7:35 and the bus comes at 7:40. The stop is five minutes away, so I always arrive just in time.

Every morning: I leave at $7:35$, the bus comes at $7:40$, the stop is $5$ min away, so I arrive at $7:40$, just in time.

$L=7:35,B=7:40,B-L=5^{\prime }\Rightarrow$ in time, $\forall$ morning.

Today the bus did not come at 7:40. I waited. At 7:50 it had still not come. The bus is late about one morning in ten.

Today: no bus at $7:40$. I waited. $7:50$: still no bus. Let $D$ = the bus is late; $P(D)\approx \frac{1}{10}$ per morning.

Today: $t=7:40$, bus $\nexists$. $t=7:50$, $\nexists$. $P(D)\approx 0.1$.

I had a choice: keep waiting, or walk. Walking to school takes twenty-five minutes. School starts at 8:15.

A choice: wait, or walk. Walk $=25$ min. School starts at $8:15$.

wait $\vee$ walk$(W)$; $W=25^{\prime }$, $S=8:15$.

If I walk now, I arrive at 8:15 exactly. If the bus comes within the next five minutes, I arrive earlier. If it comes later than that, I am late.

Walk now $\Rightarrow$ arrive $7:50+25=8:15$, exactly. Bus within $5$ min $\Rightarrow$ earlier. Bus later than that $\Rightarrow$ late.

$W\Rightarrow 7:50+25^{\prime }=8:15=S$ ✓. bus $\le 7:55\Rightarrow <S$ ✓. bus $>7:55\Rightarrow >S$ ✗.

I walked. On the way, at 7:58, the bus passed me. I was on time, and it was my own doing.

I walked. At $7:58$ the bus passed me. On time, and my own doing.

$W$. $7:58$: bus $\to$ me. $t=S$ ✓, by me.