There is a regular tetrahedron-shaped box with the numbers $1,1,1,2$ written one on each face. When this box is thrown, if the number on the bottom face is 1, region A in the figure on the right is colored, and if the number is 2, region B is colored. When the box is thrown repeatedly until both regions are colored, find the probability that the process is completed on the 3rd throw. If this probability is $\frac { q } { p }$, find the value of $p + q$. (Here, $p , q$ are coprime natural numbers.) [4 points]
There is a regular tetrahedron-shaped box with the numbers $1,1,1,2$ written one on each face. When this box is thrown, if the number on the bottom face is 1, region A in the figure on the right is colored, and if the number is 2, region B is colored. When the box is thrown repeatedly until both regions are colored, find the probability that the process is completed on the 3rd throw. If this probability is $\frac { q } { p }$, find the value of $p + q$. (Here, $p , q$ are coprime natural numbers.) [4 points]