What's the probability that two players that each throw a normal dice get their first six at the same time ?
Let $X_k,Y_k$ denote the numbers obtained with the first ($X$) and second ($Y$) dice at the $k$th try.
I'm having a hard time finding how to solve the problem. Could someone post an answer using random variables, with a detailed method, with the result ? That would really help me.
Hint: What is the chance they both get a six on the first roll? In that case you succeed. What is the chance exactly one of them gets a six on the first roll? In that case you fail. Otherwise, you are back where you started. Scale the first two up to sum to $1$ and you are there.