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Two tiles numbered $5$ and $6$ 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 smaller than $6$? 
Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
There are $2\times6=12$ different combinations. The product of two numbers is smaller than $6$ will be $5\times1$. Thus, the probability is $\frac 1{12}$. 