Elizabeth lives in San Francisco and works in Mountain View. In the morning she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home. If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she’ll use a cab exactly one time.

There are nine possible combinations as follows: bb, bc, bt, cb, cc, ct, tb, tc, tt, each having a probability of 1/9. The four combinations with a cab exactly one time are: bc, cb, ct, tc. Therefore the probability that she'll use a cab exactly one time is: 4/9.