The number of points, x, scored in a game has the probability distribution below.

the number of points obtained in one game is independent of the number of points obtained in second game. when the game is played twice, the sum of the number of points for both times could be 0, 1, 2, 3, or 4.

if y represents the sampling distribution of the sum of the scores when the game is played twice, for which value of y will the probability be greatest?