Question 8.59

image 28. Role-playing games like Dungeons & Dragons use many different types of dice. One type of die has a tetrahedral (pyramidal) shape with four triangular faces (see Figure 8.27). Each triangular face has a number (1, 2, 3, or 4) next to each of its edges. Because the top of this die is not a face but a point, the way to read it is by the number at the top of the face that is visible when the die comes to rest. Suppose that the intelligence of a character is determined by rolling this four-sided die twice and adding 1 to the sum of the results.

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Figure 8.27: Figure 8.27 Rolling a pair of tetrahedral dice: and ; , for Exercise 28.
  1. Give a probability model for the character’s intelligence. (Start with a display in the style of Figure 8.7 on page 347, adapted for the outcomes of the two rolls of the four-sided die. These outcomes are equally likely.)
  2. What is the probability that the character has intelligence 7 or higher?