If I roll a 10-sided dice and I get 6 or more as a result, I get a "success". But if I roll the dice and I get 1, it cancels one success, so that If I roll two times the dice and I get (7,1), I have 0 success, if I roll it and I get (7,2), I have one success, if I roll it and I get (1,1) I have -2 success. I am trying to compute the probability of to get at least one success. And yeah, I can have negative successes.
What I thought so far is to call A="get 6 or more" and B="to not get 1" and compute $P(A \cap B)$. But I am pretty sure is wrong since it doesn't depend of the number of times I roll the dice.
I also tried to compute it rolling the dice one time but it changes dramatically as I increase the number of times I roll the dice, and I don't understand how to describe this change.
You can choose the number of times we roll the dice. Obviously I am interested in the general case ($n$ times) but I suspect is not possible, so I would like to know the case of rolling it 5 times.