There are three colored cubes being rolled. Each cube has green, white, blue and red sides. The cubes are rolled 108 times. Calculate the probabilities of getting one green, one blue and one red dice facing up as well as the probability of getting other combinations. (please show work and your reasoning behind why we get these probabilities).

Use chi-square to calculate the goodness-of-fit.

Dice sides

Dice #1 has 3 red, 1 blue, 1 green.

Dice #2 has 2 red, 1 blue, 1 green.

Dice #3 has 1 red, 2 blue, 2 green.