Two fair yellow dice have an equal number of faces numbered 1 to y. When both dice are rolled, what sum will appear most frequently? What is the probability that the sum appears? Explain your answers.

Extension:
A yellow die has y faces numbered 1 to y, and a green die has g faces numbered 1 to gg and y are different integers. When both dice are rolled, what sum will appear most frequently? What is the probability that the sum appears? Give your answers in terms of g and y. Explain your answer.