I am solving one question like this
A fair die is rolled repeatedly, and a running total is kept (which is, at each time, the total of all the rolls up until that time). Let pn be the probability that the running total is ever exactly n (assume the die will always be rolled enough times so that the running total will eventually exceed n, but it may or may not ever equal n).
the question is
Give an intuitive explanation for the fact that p(n) <- 1/3.5 = 2/7 as n = infinity.
the explanation is below,
An intuitive explanation is as follows. The average number thrown by the die is (total of dots)/6, which is 21/6 = 7/2, so that every throw adds on an average of 7/2. We can therefore expect to land on 2 out of every 7 numbers, and the probability of landing on any particular number is 2/7.
That's the line I don't get it, why we can transfer