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 violet, amber. Their branch probabilities are \(\text{violet}: \frac{1}{2}\), \(\text{amber}: \frac{1}{2}\)

At the second stage, the possible outcomes are violet, amber, white. Their branch probabilities are \(\text{violet}: \frac{1}{3}\), \(\text{amber}: \frac{1}{3}\), \(\text{white}: \frac{1}{3}\)

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

Let \(E\) be the event that exactly one stage outcome is amber