Each of the six sides of a dice is marked with one of the numbers $1,2,3,4,5,6$. The numbers are chosen at random and independently. The dice is thrown twice. What is the probability that the two throws show the same number?
Choosing one out of six, is done with the probability $1/6$. A dice shows a certain side upp also with probability $1/6$. So for example, the probability of choosing the number $1$ and then throwing a number $1$ is $1/6\cdot 1/6=1/36.$
I'm trying to solve this by drawing a tree diagram. For the first throw, the probability to get a certain number is $6\cdot 1/36=1/6$, and to get the same number on the second throw is then $1/6\cdot 1/6 = 1/36.$
The correct answer is $11/36.$ What am I missing?