Student: Date: Probability: Everyday Decisions Based on Probabilities Driving and Risk Javier will be a high school senior next year. He wants to get a vehicle to celebrate his graduation. Javier's mother researched vehicle safety and found that 1 of every 6 teenage drivers was involved in some kind of accident. While talking to his math teacher, Javier mentioned that he did not think the risk was high enough to be concerned. Javier decided to survey 500 students, 230 of whom were male, to help him convince his mother to allow him to get a vehicle. No student has both a car and a motorcycle. The following are the data from Javier's survey: Car Motorcycle Males with vehicle 150 23 Males involved in accident 40 6 Females with vehicle 225 10 Females involved in accident 15 4 1. Draw a Venn diagram and a tree diagram of the data. 2. Using the data, what is the probability that Javier will be involved in an accident if he gets a motorcycle? Explain your reasoning. 3. Based on these survey data, Javier told his mother that he only has a 1% chance of getting in an accident. Is he correct? Why or why not? 4. Use your Venn diagram to write three facts that help Javier convince his mother to let him get a vehicle. 5. What probability model would you advise Javier to use when he tries to convince his mother? 6. REFLECTION: List some advantages and disadvantages for each type of model used in this problem. 7. EXTENSION: Research your favorite vehicle's safety measures and its likelihood of being involved in an accident. Prepare a short presentation of your findings. Charles A. Dana Center at The University of Texas at Austin Advanced Mathematical Decision Making (2010) Activity Sheet 6, 2 pages 16