Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 1 / 7 / b / i

For $B$ to make a first throw, $A$ must first pass, with probability $1/2$. For $B$ then to win on that throw, $B$ must roll one of two winning faces, with probability $1/3$. The throws are independent, givingA first throw of $3$ by $A$ would make $B$ win without throwing, and is excluded by the requested event.