In the board game Dead of Winter, certain actions a player can take result in rolling a 12-sided die. On one face of the die, there's a tooth, representing instant death by zombie. Two faces of the die result in a frostbite wound, and three faces of the die result in a regular wound. Half the time one rolls the die, there is no effect. Suppose the game calls for a player to roll the die three times in a row. Assume that if a tooth is rolled, death occurs and no further rolls are made. Assume also that if three wounds of any kind are rolled, death occurs. What is the probability that a player rolling the die three times escapes death?
I tried (11/12)(11/12)(6/12), but I don't think that this accounts for the order of the die. For example, if I rolled a non-wound on the second roll, wouldn't that change my third probability?