Ava, Lucero, and Vinh are playing a game involving a single $6$-sided die. The rules are as follows:

* Ava rolls first. If she rolls a $1,$ or $2,$ then she wins.

* Otherwise, Lucero rolls next. If Lucero rolls a $4$ or a $5,$ then she wins.

* Otherwise, Vinh rolls next. If Vinh rolls a $3$ or $6$ then he wins.

* Otherwise, the turn passes back to Ava, with the same rules.

Calculate the probability that Vinh wins.

gnistory Oct 30, 2024