If I enter a friend's house and he has rolled a dice (d6) on a table which has a value $1$, he asks me the following,
"Do you think I rolled this dice once and got $1$ or do you think I rolled it multiple times and got $1$ ?"
Intuitively I choose the latter, but I maybe wrong. How do you do the math for this?
On
Rule 1. You roll the die once and that is your final result. Rule 2, You roll the die until a 1 appears. Unless you know the probability of one rule being in place as opposed to the other, there is no way this problem can be answered. Furthermore you also have to ask the question,what is the probability that this question would have been posed to you,if any number other than 1 had appeared on the first roll.
Mathematically, the roll of a die is called independent, which means it is not affected by the roll that came before or after it.
There is no answer to this question. The die was rolled once and landed on 1, but the amount of times he rolled it before has no bearing on the final roll.
That said, the math may not be the full picture here. If you want to bring psychology in to the picture, then you would have to consider if he intended to roll a 1. Since the chance of rolling a 1 is $\frac{1}{6}$, you would expect that he rolled the die three times in order to get the result he wanted.