A bus arrives at a stop every 12 minutes, without a break, and you reach the stop at a random…

For a point chosen at random on a line, $P = \dfrac{\text{good length}}{\text{total length}}$. For two numbers chosen at random in $[0, a]$, the sample space is a square of side $a$, and $P = \dfrac{\text{good area}}{a^2}$. A simulation estimates a probability, with a usual error of about $\sqrt{\dfrac{p(1 - p)}{N}}$.