1. D&D players know very well that dice come in different varieties. One particular type is a four-sided polyhedron called a tetrahedron. Imagine that each face is equally likely to land face down, and that you roll the die three times. On each roll consider only whether a 1 lands face down or it doesn't. (a) Identify the sample space for a single roll of the die. (b) Let X be the number of times a 1 lands face down in three rolls, identify the sample space for X. (c) Construct the probability distribution for X (use binompdf). (d) Using the probability distribution from part (c), determine the probability of rolling at least two 1's face down. (e) What is the probability of rolling at most two 1's