m118 Homework 6 (4.1) Name: Please work all problems and show your work. Remember, an answer with no justification is no answer. Based on concepts from Section 4.1 (Basic Probability Formula, Union Formula, Odds, Venn Diagrams) 1) Sterling is planning to visit Miami, Chicago, Denver, Indianapolis and Houston. Find the probability that he visits Miami and Chicago in consecutive stops. 2) Crispin and his friend Glover are taking a picture with 4 other people standing in a row. Find the probability that: (a) Crispin is at one end and Glover at the other. (b) Crispin and Glover will be standing next to each other (in either order). 3) A number is selected from the set {1,2,3,4,5,6,7,8,9,10,11}. What is the probability that it is less than 4 or odd? 4) Events A and B are disjoint. Pr[A]=0.15 and Pr[B]=0.45. Find Pr[ A B] 5) A set is partitioned into 3 subsets: A, B, and C. If C is three times as likely as A, and B is two times as likely as C, Find the probability of C. 6) A committee consists of 8 males and 12 females. If 5 people are chosen at random to be on a subcommittee, what is the probability that at least one person from each sex is chosen? 7) Five cards are selected from a fair deck. What is the probability that they contain: (a) exactly 3 red? (b) at least 4 red? (c) the same color? (d) more than one suit? 8) The probability of winning a game is 0.20. Find the odds against winning (odds for losing). 9) The odds in favor of winning a game are 7:5. What is the probability of: (a) winning a game? (b) losing a game? 10) Out of 90 law students surveyed, 30 took Intellectual Property Law, 40 took Probate Law, and 10 took both. What is the probability that a student: [Hint: Use a Venn Diagram] (a) Took exactly one of the classes? (b) Neither of the classes? (c) At least one of the classes