Tree Diagrams

Late then on time: $\displaystyle 0.2 \times 0.8 = 0.16$
On time then late: $\displaystyle 0.8 \times 0.2 = 0.16$
$\displaystyle 0.16 + 0.16 = 0.32$

Red then blue: $\displaystyle \frac{5}{8} \times \frac{3}{7} = \frac{15}{56}$
Blue then red: $\displaystyle \frac{3}{8} \times \frac{5}{7} = \frac{15}{56}$
$\displaystyle \frac{15}{56} + \frac{15}{56} = \frac{30}{56} = \frac{15}{28}$

'At least one' covers many separate outcomes, which would each have to be worked out and added.
Its opposite is the single outcome 'none at all', so it is far quicker to find that one probability and subtract it from $\displaystyle 1$.