$1.$ A die used in a certain board game has eight faces, of which $3$ are red, $3$ are yellow, and $2$ are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die $3$ times before blue lands faceup