Die Normal Red Grime Side 1Side 2 Side 3|Side 4 Side 5 Side 6MeanRoll 3.5 3.5 3.5 3.5 Green Grime 2 Blue Grime 1 2. You roll four dice: one white regular six-sided die, and three Grime dice (one red, one blue, (a) Describe what a "state" would be and the ensemble that represents the situation. How (b) If the sum of the faces of the four dice is known to be 14, what ensemble best represents (c) Assuming the total roll is 14 as in part (b), what are the probabilities P,..., Ps for the and one green), with the faces of each die shown in the table above. many bits of information are missing? the situation, and how many bits of information are still missing? various faces 1-6 of the white die? How much missing information is associated with this probability distribution? (d) Find a numerical value for the ratio of the answer to part (c) to the answer of part (b). If this ratio is not equal to 1/4, explain why it makes sense that the missing information associated with 1 of the 4 dice is more (or less) than 1/4 of the total. Die Normal Red Grime Side 1Side 2 Side 3|Side 4 Side 5 Side 6MeanRoll 3.5 3.5 3.5 3.5 Green Grime 2 Blue Grime 1 2. You roll four dice: one white regular six-sided die, and three Grime dice (one red, one blue, (a) Describe what a "state" would be and the ensemble that represents the situation. How (b) If the sum of the faces of the four dice is known to be 14, what ensemble best represents (c) Assuming the total roll is 14 as in part (b), what are the probabilities P,..., Ps for the and one green), with the faces of each die shown in the table above. many bits of information are missing? the situation, and how many bits of information are still missing? various faces 1-6 of the white die? How much missing information is associated with this probability distribution? (d) Find a numerical value for the ratio of the answer to part (c) to the answer of part (b). If this ratio is not equal to 1/4, explain why it makes sense that the missing information associated with 1 of the 4 dice is more (or less) than 1/4 of the total