(Simple) probability questions

[littlejon]

Hi guys, I have a couple of questions I was asked in an interview:

1) You roll a pair of fair dice. If no 6 appears, you keep rolling both until at
least one 6 appears. What is the probability that when you stop, both dice show 6s?
2) I roll a pair fair dice. I choose one of the two dice at random
and tell you the result, e.g. “I have rolled at least one 3”. What is the probability from your
point of view that I have rolled a double (in the example, a double 3, of course)?

My answer to both questions was P=1/11. My approach was that in both cases the sample space was reduced from 36 possibilities, to 11.

One of the answers was wrong, but this was an online test and I wasn't told which. Can someone help me figuring which?

Thanks

 

[bigbadwolf]

The first should be 1/11 and the second 1/6.

 

[littlejon]

The first should be 1/11 and the second 1/6.

Damn it, you're right. Thanks. I feel like an idiot now. Can't believe how when you get something in your head its hard to think differently.