Problem solving rolling dice

Question

You are rolling two fair dice, and you are blindfolded, after a certain roll, your partner tells you that you have rolled at least 9.

1. What is the probability that you have rolled at least 11?
2. What is the probability that you have actually rolled an 11?

Answer 1

If you have rolled in at least $9$, then the possible outcomes are $(4,5),(5,4),(6,3),(3,6),(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)$ i.e. there are $10$ possible outcomes.

If you have rolled in at least $11$, then the possible outcomes are $(5,6),(6,5),(6,6)$ i.e. there are $3$ possible outcomes.

If you have rolled in exactly $11$, then the possible outcomes are $(5,6),(6,5)$ i.e. there are $2$ possible outcomes.

So the probability in case (1) is $\frac{3}{10}$. And the probability in case (2) is $\frac{2}{10}=\frac{1}{5}$.