Modelling the probability distributions of dice

If you have ever played the game of Catan you’ll quickly realise that when rolling two dice the number 7 is very common! This brought up a question, which is as follows:

What is the true probability of rolling a sum of 7 with two 6-sided dice? Moreover, what is the probability of rolling a sum of any number with 6-sided dice?

Here is what I did to find the answers.

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