Confusing probability question I have got a task, which seems a quite confusing for me. It is simple: In a market, they sell eggs in egg holders, they store $10$ of them in each. There is $60$% chance, that all of the eggs are ok, $30$% chance, that exactly $1$ of them is broken, and $10$% chance, that exactly $2$ of them are broken(it is random, which one is broken).
We buy an egg holder, and after we grab our first egg, we are sad, because it is broken. What is the probability, that there is one more broken egg in our holder?
The "logical" way would be: $30$% of them have $1$ broken egg, $10$% of them have $2$, so, to have $2$ broken, the chance must be $\frac14$. But I am not really sure if that is the correct approach, since the broken egg can be anywhere, getting a broken one for first may be not that easy, or is that independent?(Maybe, I could use Bayes Theorem somehow)?
Any help appreciated.

I see this as analogous to the pancake problem ... specifically, I would argue that having randomly observed a broken egg, the chances that you are in case C have disproportionately increased.  
Imagine that you had $100$ of your cartons, $60$ of type A, $30$ of type B, and $10$ of type C.  You select one egg randomly from each.  You'll get $3$ broken ones from the Bs and $2$ from the Cs.  Hence your probability is $\frac 25$.
