Be sure to show your work: Can you compute the request directly? OR do you need to explain further? State the original request, e.g. P(BOE) e.g. P(MA) = P(M) * P(A|M) 35 Show how you are using the given information to compute your answer, e.g. 92 Provide a numerical answer to four decimal places; e.g. 0.3804 Problems #1, #2, and #3 Drive With Us Auto Insurance Drive With Us Auto Insurance classifies its customers as good risk, average risk, and poor risk. Good risk drivers have a 7% chance of an accident over a one-year period; average risk drivers have an 18% chance of an accident; poor risk drivers have a 33% chance. The clientele base in the Rochester office of Drive With Us is 30% good risk, 45% average risk, and 25% poor risk, and is assumed to have the same accident rates as the national clientele of Drive with Us. Consider randomly selecting a client from the Rochester office. Problem #1 A. What is the probability that the client is a good risk and has had an accident in the past year? SHOW YOUR WORK. B. What is the probability that the client has had an accident in the past year? SHOW YOUR WORK. Problem #2 A. If the client has had an accident in the past year, what is the probability that he is a poor risk client? SHOW YOUR WORK. B. If the client has NOT had an accident in the past year, what is the probability that he is a poor risk client? SHOW YOUR WORK. Problem #3 Write sentences to describe the probability that a randomly selected driver is poor risk. With no information about the past year. Knowing that the driver had an accident in the past year. Problems #4 and #5 Upright Freezers An appliance dealer sells three different models of upright freezers having 14.1, 17.7, and 20.5 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by a randomly selected freezer customer. X 14.1 17.7 20.5 p(x) 0.30 0.48 0.22 Problem #4 A. E(X) Compute E(X). SHOW YOUR WORK. Write a sentence to interpret its value. B. SD(X) Problem #5 Compute SD(X). SHOW YOUR WORK. Write a sentence to interpret its value. The price of a freezer having capacity X cubic feet is Price 52X-135 dollars. A. Compute E(Price). SHOW YOUR WORK. B. Compute SD(Price). SHOW YOUR WORK. Problem #6 System of Independent Components (think back to week 1) The system below consists of 5 components, arranged in three sub-systems. Each sub-system has a particular type of component, with a given failure rate. Sub-System 1-2: Components 1 and 2 each have a probability 0.02 of failure. Sub-System E: Component E has a probability 0.03 of failure. Sub-System x-y: Components x and y each have a probability 0.05 of failure. The components all work independently of each other. . 2 E Be sure to SHOW YOUR WORK for each question below. A. Consider Sub-system 1-2 by itself. What is probability of failure for the sub-system? What is probability of success for the sub-system? B. Consider Sub-system E by itself. X y . What is probability of failure for the sub-system? What is probability of success for the sub-system? C. Consider Sub-system x-y by itself. What is probability of failure for the sub-system? What is probability of success for the sub-system? D. Now consider the entire system with all three sub-systems. What is the probability of system failure? SHOW YOUR WORK.