Sigma-algebra

Section I: Events and Probabilities 4 Fig 1. Rolling a 4 on a D4 A four sided die (D4), shaped like a pyramid (or tetrahedron), has 4 flat surfaces opposite four corner points. A number (1, 2, 3, or 4) appears close to the edge of each flat surface. When rolled, the D4 comes to rest on one of its flat surfaces. The outcome of the roll is the number associated with the flat surface onto which the D4 comes to rest. An example D4 roll resulting in a 4 is depicted in Figure 4. 1. Write out the dense sigma-algebra for events concerning rolling a D4 (10 points) 2. For the dense sigma-algebra, not including the empty set O or its negation, event E = {1,2,3,4), if you were playing a guessing game involving the roll of a D4, what is an example of the easiest event to guess (if there is more than one, pick one)? Describe what makes it the easiest? (5 points) 3. What is an example of the hardest event to guess (if there is more than one, pick one)? Describe what makes it the hardest? (5 points) 4. What is the probability of the hardest event to guess? Show your work. (5 points) 5. What is the probability of the easiest event to guess? Show your work (5 points)