A pair of fair dice is thrown. What is the probability of getting a six on both, given at least one die gets six?

Let $A$ be the event "at least one die is 6" and $B$ be "both dice are 6".Event $A$: $(1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(6,1),(6,2),(6,3),(6,4),(6,5)$. Total outcomes in $A=11$.Event $B\cap A$: $(6,6)$. Total outcomes = 1.Conditional Probability $P(B|A)=\frac{n(B\cap A)}{n(A)}=\frac{1}{11}$.