Two fair dice are rolled. find the probability of a "double" given that the sum is 11.

Star with the statement: "Given that the sum is 11"

which may seem a bit odd considering its the last part of the problem

The "given" is important as it sets up the constraints of what we're dealing with. In this case, we know 100% (we can see or someone told us without lying) that the sum is 11. We don't know what the individual values are but we know they add to 11.

What are the ways to add to 11? Well they are ...

5+6 = 11

6+5 = 11

so there are 2 ways to do it. As you can see, none of those ways involve a double. A double is where we have two of the same values (eg: snake eyes which is 1 and 1 giving 1+1 = 2 as the sum). It turns out that it's impossible to have doubles add to any odd number.

So if we know the sum is 11, and we're asking "what is the probability of rolling doubles", then the answer is 0.

The 0 indicates "impossible" or "certainty of it never happening".