Question 11
Alice is at the origin $(0,0)$ of the coordinate plane. She moves according to the roll of a standard cubical die. If the die rolls is 1, she moves 1 space to the right. If the die rolls is 2 or 3, she moves 1 space to the left. If the die rolls is 4, 5 or 6, she moves 1 space up. What is the probability that after four moves, Alice lands on the point $(1,1)$ for the first time?