Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 2 / 10E / a / Solution

Ignore rolls showing $2,3,4,5$ and consider the first roll among $\{1,6\}$. By symmetry, the event $A$ that a 1 occurs before a 6 has probability $1/2$. The event that the very first roll is 1 has probability $1/6$ and is contained in $A$. Hence