7.3 1. Write a sample space for the following: a box contains five balls numbered 1,2,3,4, and 5. A ball is drawn at random, the number recorded, and the ball is replaced. The box is shaken, a second ball is drawn, and the number recorded. 2. Write out a sample space S and find n(S) for the following experiment: a student takes a three-question true/false quiz and guesses on all three questions, so each answer is equally likely to be correct or wrong. 3. A single fair six-sided dice is rolled. What is the probability of getting a number greater than 2? 4. A card is drawn from a well shuffled 52-card deck. What is the probability of draw- ing a spade or a king? 5. Three unusual dice, A, B, and C, are constructed where A has faces 3, 3, 4, 4, 8, 8; B has 1, 1, 5, 5, 9, 9; and C has 2,2,6, 6, 7, 7. When rolling the die, we say the one with the higher outcome beats the other. a) Find the probability that B beats A b) Find the probability that C beats B c) Find the probability that A beats C d) Which die is the best choice? Why? 6. Two dice are rolled. Find the odds in favor of rolling: a) A sum of 3 b) Not a sum of 6 7. The probability that a company makes a profit this yeas is .74. a) Find the probability the company will not make a profit this year. b) Find the odds against the company making a profit this year.