Suppose you have three dice, colored red, green, and blue, with a very unusual set of...

 

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Suppose you have three dice, colored red, green, and blue, with a very unusual set of numbers written on each. Rather than merely displaying the numbers 1 through 6, the six sides of the dice show the following: Red: 3,3,3,3,3,6 Green: 1,4,4,4,4,4 Blue: 2,2,2,5,5,5. (a) What is the probability that red beats green? What is the probability that green beats blue? What is the probability that blue beats red? What do you notice about this pattern? (b) Suppose you roll two blue dice against two red dice. What is the probability that the sum of the blue dice is greater than the sum of the red dice? Suppose you have three dice, colored red, green, and blue, with a very unusual set of numbers written on each. Rather than merely displaying the numbers 1 through 6, the six sides of the dice show the following: Red: 3,3,3,3,3,6 Green: 1,4,4,4,4,4 Blue: 2,2,2,5,5,5. (a) What is the probability that red beats green? What is the probability that green beats blue? What is the probability that blue beats red? What do you notice about this pattern? (b) Suppose you roll two blue dice against two red dice. What is the probability that the sum of the blue dice is greater than the sum of the red dice?