Yana and Zahid are playing a game. Yana rolls her pair of fair six-sided dice and draws a rectangle whose length and width are the two numbers she rolled. Zahid rolls his pair of fair six-sided dice, and draws a square with side length according to the rule specified below.
a. Suppose that Zahid always uses the number from the first of his two dice as the side length of his square, and ignores the second. Whose shape has the larger average area, and by how much?
b. Suppose now that Zahid draws a square with the side length equal to the minimum of his two dice results. What is the probability that Yana’s and Zahid’s shapes will have the same area?
c. Suppose once again that Zahid draws a square with the side length equal to the minimum of his two dice results. Let D= AreaYana - AreaZahid be the difference between the area of Yana’s figure and the area of Zahid’s figure. Find the expected value of D.