The area under a probability distribution function, or pdf, always works out to 1, reflecting the fact that the probability of getting an outcome somewhere in the sample space must necessarily equal 1. We can then find the probabilities of getting outcomes in specific intervals of the sample space by calculating the area under the pdf over those intervals.
The base of the shaded rectangle is length 2, since it goes from 9 to 11.
The height of the rectangle is 1/5. Why? Well, the pdf goes from 8 to 13 (hence length 5), and since it's uniform it's a rectangle (the question assumes we already realize this). Since it's a pdf, the area must be 1. So, a rectangle with length 5 and ... what height?... has area 1. Basic algebra reveals that this height must be 1/5.
The area of the shaded rectangle (not the whole rectangle, which has area 1 as mentioned above) is 2*1/5 = 2/5. And this means that the probability of waiting between 9 and 11 minutes is 2/5.
Bonus question: Do you feel that this is a realistic model of bus wait times? For instance, according to this model, there's a 40% chance of waiting between 9 and 11 minutes, but a 0% chance of waiting between 6 and 8 minutes, and also a 0% chance of waiting between 13 and 15 minutes. It would have to be a pretty precisely run bus line to have such a large difference in probabilities for two-minute intervals that aren't particularly far apart.
