6. Consider Efron's non-transitive dice where the 6 faces for each die are given in the table below: Die A 0 0 4 4 4 4 Die B 3 3 3 3 3 3 Die C 2 2 2 2 6 6 Die D 1 1 1 5 5 5 a. Suppose that there are 4 players in the game, and each player will choose one die and roll it. The largest number will win. For each die, calculate the probability that the largest number observed occurs on that die. Which die / dice would you choose? , b. Suppose that there are 4 players in the game and each will choose one die and roll it. The person who rolls the smallest number will be eliminated. For each die, calculate the probability that the smallest number observed occurs on that die. Now, which die / dice would you choose. Of course, we are assuming that you want to stay in the game (rather than grading papers, or washing windows). C. Suppose that, in the 4 player game, the person who rolls the smallest number pays $5 to the person who rolls the largest number. Calculate each player's expected gain after one round. d. Suppose that the person with die A loses the first round and is eliminated. The three remaining players play another round with the remaining dice. Again, the person who rolls the smallest number pays $5 to the person who rolls the largest number. Calculate each player's expected gain from this round