Math 245 Lab D sec 6.4-6.6 Your name:__________________________ Recitation time: ______ 1. Decide which formula you would need to use to solve each of the following problems, either the conditional probability formula from section 6.4 or Baye's rule from section 6.6. Explain your decision and label all the events as they correspond to the event names in the formula you choose. (You do not need to solve the problems.) a) At an auto inspection station, 68% of the vehicles are cars and 32% are pickups. The inspection records show that 14% of the cars and 23% of the pickups fail to meet the pollution standards. If a vehicle fails to meet the standards, find the probability it is a car. b) The 106th U.S. Senate was composed of 55 Republicans and 45 Democrats. An amendment proposed by the president was supported by 80% of the Democrats and by 20% of the Republicans. Find the probability that a person who supported the amendment is a Republican. c) In a group of college students, made up of 60 males and 75 females, 35% of the males and 40% of the females are from out of state. If a student is randomly selected and found to be male, find the probability the student is from out of state. 2. A survey of math students at a college revealed that 43% consistently spent at least 1.5 hours on each homework assignment and 57% consistently spent less time than that. Of those students who spent at least 1.5 hours on homework, 78% earned an A or a B in the course. Of those who spent less than 1.5 hours, 21% earned an A or a B in the course. A randomly selected math student earned an A or a B in his/her math course. Find the probability the student spent at least 1.5 hours on homework. a) Explain why you need to use Baye's rule to solve this problem. d) To use Baye's rule you need to choose appropriate notation for your different events so you can use the formula correctly. Fill in the blanks below. Your event that you know the outcome for is F : ________________________________. Your partition is E1 : _________________________ and E2 : __________________________. You are trying to calculate the conditional probability P( ___ | ____). e) Find each probability you will need for the Baye's rule formula. P(E1) = P(E2) = P(F|E1) = P(F|E2) = f) Now use Baye's rule to get your final answer. PE1 F PE1PF E1 PE1PF E1 PE 2PF E 2 _____ ______ ___ ___ ____ ____ g) Write your final answer in the context of the