Finding probability using Volume fraction A bus line runs every $30$ minutes. If a passenger arrives at a stop randomly, what is the probability that he will have to wait more than $10$ minutes for the next bus?
I solved this using probability distribution and I got the answer $\frac {2}{3}$ which is correct.
But I am told to solve this using volume fraction over some domain. In my attempt for doing this, I get a different answer $\frac {1}{12}$
Can anyone show me what I'm doing wrong here?

 A: I don't know what the other person meant by "volume fraction over some domain", unless they meant a $1$-dimensional volume, i.e. an interval.
The only random variable is $W = $ waiting time, which is $U(0, 30)$.  This is the interval $(0, 30)$, of length $30$.
The event $W > 10$ is presented by the sub-interval $(10, 30)$, of length $20$.
Therefore, answer $= 20 / 30 = 2/3$.

It seems (I'm guessing here) you wish to introduce more variables.  E.g. Let $B = $ bus arrival time (modulo $30$ minutes, e.g. counted as time since the last exact hour or exact half-hour on the clock) and $P = $ passenger arrival time (similarly modulo $30$ minutes).  Then the state space ("volume") is $30 \times 30$ (not $30 \times 20$ as you drew).  Now waiting time $W = B - P$ (modulo $30$).  Draw the two parallel lines $W=0$ (you didn't draw this) and $W=10$ (you drew this) and note that the latter line "wraps around".  The narrow band between the two lines represent $W < 10$ and the complement area $W > 10$.  You should find that the complement has area $600$ so the answer is still $600/900 = 2/3$.
A: @antkam I understood your explanation clearly. Thanks a lot. I also tried to solve it in a way. Can you see if I'm wrong somewhere in this attempt.

