see the assignment attached. PROBLEM 2 (25 points): In a study of marriages, researchers examined the faithfulness of men and the survival of the marriage. The results for 5,000 marriages were as follows: Faithful (F) Unfaithful (F’) Divorce (D) 1300 1200 2500 No Divorce (D’) 1700 800 2500 3000 2000 5000 If an individual man is selected at random, what is the probability that he or she a) is divorced? b) Is divorced given that he was faithful? c) is divorced and unfaithful? d) is divorced or faithful? e) Is there a relationship between faithfulness and divorce? PROBLEM 3 (15 points): Olympic Medals The medal distribution from the 2004 Summer Olympics games for the top 23 countries is shown below: Gold Silver Bronze United States 35 39 29 Russia 27 27 38 China 17 32 0 Australia 17 16 16 Others 133 153 136 a) Find the probability that the winner won the gold medal, given that the winner was from the United States. b) Find the probability that the winner was from the United States, given that she or he won a gold medal. c) Are the events “medal winner is from United States” and “gold medal won” independent? Explain PROBLEM 4: Religion and Divorce (20 points) What is the probability of being divorced? What is the probability of being a divorced Catholic? What is the probability of being divorced given that one is Jewish? Is there a relationship between divorce and religion? Protestant Catholic Jewish Been Divorced 400 200 100 Never Divorced 600 500 200 PROBLEM 5 (30 points): given in a previous midterm Some collected data is presented in the table below: Age Team {18-20} {21 – 25} {26-30} Above 30 Jumping High 6 10 11 8 Speedy Skies 3 15 20 20 Winter Fun 18 10 8 6 Give the literal formula first (not with numbers) and then solve: “What is the probability of being a Winter Fun member given that you are in the {26-30} age category” Give the literal formula first (not with numbers) and then solve: “What is the probability of being a Speedy Skies member of 29 years old” Give the literal formula first (not with numbers) and then solve: “What is the probability of being younger than 26 years (either in {18-20} or {21-25}) given that you are a member of Jumping High team”. Give the literal formula first (not with numbers) and then solve: “What is the probability of being a member of Jumping High or a member of Speedy Skies team. Give the literal formula first (not with numbers) and then solve: “What is the probability of not being a member of Jumping High team” Is there any relationship between being in {18-20} age category and belonging to a specific team? (relationship between age and team)