If you randomly choose your ride twice, what's the probability that you'll use a cab exactly one time?

Question

In the morning, you have 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same choices.

Answer 1

There are 9 options total: 3 for the morning ride times 3 for the evening ride.

Of these, 2 involve a cab in the morning and a bus or train in the evening, while 2 involve a cab in the evening and a bus or train in the morning.

So there are 4 options with exactly one cab ride. Since all options are equally probable, we get the probability 4/9 as our final answer.