Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 8 / a / i / Solution

The single-roll colour probabilities are $1/2$, $1/3$ and $1/6$. There are $3!$ possible orders of the three distinct colours, and the independent rolls give each order probability $(1/2)(1/3)(1/6)$. The events are disjoint, so the required probability is