Probability of 2 dice hitting a certain number exactly using as many rolls as you want?

Question

Sort of an easy question (answer is intuitive)

Original problem:

http://answers.yahoo.com/question/index;_ylt=Auxvhgf1BqOObdOC26wMgioAAAAA;_ylv=3?qid=20080828220525AAyQ3Wy

You roll 2 dice at a time. What is the probability of getting exactly n, where n is large, using as many rolls as you want?

Answer 1

The probability of getting exactly n, where n is large, using as many rolls of two dice as needed is 0.142857'

(Where an apostrophe denotes repetition of the digits between the apostrophe and the decimal point).

Proof:

It should be clear that the probability of getting any large number is equal (i.e. the distribution becomes uniform as n increases).  Since, on average, rolling two dice will advance seven spaces, the probability of getting any one number is 1/7 or 0.142857'

Test:

Using a small C++ program (TwoDiceOneNumber.cpp), data collected confirmed that the probability was indeed 1/7.