Represent a multi-stage finite sample space

A finite experiment has 2 stages. The stage choices are independent

At the first stage, the possible outcomes are medium, small, large. Their branch probabilities are \(\text{medium}: \frac{1}{3}\), \(\text{small}: \frac{1}{3}\), \(\text{large}: \frac{1}{3}\)

At the second stage, the possible outcomes are medium, small. Their branch probabilities are \(\text{medium}: \frac{1}{2}\), \(\text{small}: \frac{1}{2}\)

Let \(S\) be the sample space of ordered stage outcomes

Let \(E\) be the event that the first-stage outcome is small