Two tiles numbered $1$ and $2$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is greater than or equal to $12$? 
选项为:A:$\frac {1}{2}$  B:$\frac {1}{6}$  C:$\frac {1}{3}$  D:$\frac {1}{4}$  E:$\frac {1}{12}$  请回答其中一个选项.