Show your calculation and give your answer in the fraction form and in the decimal form (to 4 digits) to receive full credit. Part 1: Let's play \"Craps\" (6 points) A favorite casino game of dice \"craps\" is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results ina 2 or 3 (called \"craps\") the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits. b. o o B nl B B List the possible outcomes (sample space) for winning on the first roll of the dice. What is the probability that a player wins the game on the first roll of the dice? List the possible outcomes (sample space) for losing on the first roll of the dice. What is the probability that a player loses the game on the first roll of the dice? If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll? If the player throws a total of 6 on the first roll, what is the probability that the player loses in the next roll? Part 2: Which Mortgage to Choose? (12 points) 210322 Franklin University Math215 Statistical Concepts Name: A title company wants more information about mortgages based on the type of home being bought. 1000 mortgages are randomly selected. The sample results in the table below shows the number of mortgages funded based on the type of home purchased. Answer the following questions. Include your answers in fraction and in decimal forms and round your decimal answers to 4 digits. Single-Family Condo Multifamily Total Adjustable 400 Fixed 90 300 Total 200 1000 Fill in the remaining cells in the above table with your own numbers ensuring rows sum to row totals and columns sum to column totals. In addition, the row and column totals will both sum to the grand total of 1000. Answers will and should vary. The following questions will use the numbers (already existing or added by you) in this table. Fill in the table cells very carefully and use this table to answer the following questions. a. What is the probability that the mortgage is Adjustable AND for a Single Family? b. What is the probability that the type of home purchased is a Condo? c. What is the probability that the mortgage is Fixed OR a Single-Family home is purchased? d. Given that a Condo is purchased, what is the probability the mortgage is Adjustable? e. Given that the mortgage is Adjustable, what is the probability that a Condo is purchased? f. Determine if type of mortgage and home purchased are independent. Justify your answer by showing your work here. (HINT: Use the Multiplication Rule or conditional probabilities from above) g. Determine if purchasing a Single-Family home and a Condo are mutually exclusive events. Justify your answer using probabilities. In problems below, all probabilities must be calculated using a Ti83 or TI184 calculator or MS Excel. Be sure to list the calculator function in its entirety or the Excel command as your work for each problem. List the formulas for the mean and standard deviation as your work for those calculations as appropriate. Part 3: Fender Bender (12 points) The article, \"Should You Report That Fender-Bender?\" (Consumer Reports, 2013:15), reported that 7 in 10 automobile accidents involve a single vehicle. A random sample of 25 accident reports is selected. Answer the following questions. Include your calculator functions or Excel commands for each probability guestion and round your answers to 4 digits. a. What s the probability that exactly 8 accidents involve a single vehicle? b. What s the probability that at most 13 accidents involve a single vehicle? c. Whatis the probability that at least 5 accidents involve a single vehicle? d. Whatis the probability that fewer than 15 accidents involve a single vehicle? e. What is the probability that more than 18 accidents involve a single vehicle? f. Find the mean and standard deviation of the accidents that involve a single vehicle. Show your formula setup and your work. Use proper symbols