1. List the elements of each of the following sample spaces: (a) the set of integers between 1 and 50 divisible by 8; (b) the set = {x:+4x-5=0}; H (c) the set of outcomes when a coin is tossed until a tail or three heads appear; (d) the set = {1:1 is a continent }; (e) the set = {z2z-420 and 1 <1}. I 2. An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space 12. 3. Let A. B, and C be events relative to the sample space f. Using Venn diagrams, shade the areas representing the following events: (a) (AB) (b) (AUB) (c) (ANC)UB 4. Which of the following pairs of events are mutually exclusive? (a) A golfer scoring the lowest 18-hole round in a 72-hole tournament and losing the tournament. (b) A poker player getting a flush (all cards in the same suit) and 3 of a kind on the same 5-card hand. (c) A mother giving birth to a baby girl and a set of twin daughters on the same day. (d) A chess player losing the last game and winning the match. 5. A statistics class for engineers consists of 25 industrial, 10 mechanical. 10 electrical, and & civil engineering students. If a person is randomly selected by the instructor to answer a question, find the probability that the student chosen is (a) an industrial engineering major (b) civil engineering or an electrical engineering thajor