The student's tree diagram shows the various possible outcomes at each stage and labels them with a weight, or probability of happening. If the diagram is drawn neatly, it is clear that the sum of the different probabilities at any given stage is 1. The diagram also helps make clear which probabilities need to be added or multiplied in the problem-solving tasks. And the situation shows why it is reasonable to multiply. For example, the probability of starting in Northside, going to Downtown, and then going to Southside can be thought of as "20% of the time a cab will go from Northside to Downtown, and then 50% of the cabs in Downtown will go on to Southside, so the probability is 0.5 times 0.2, or 10%.

The answer to the probability question comes from the sum of a number of probabilities and can't be calculated using a basic formula. A representation helps ensure that all of the appropriate probabilities are multiplied and then added.