a) An automobile manufacturer is concerned about a possible recall of its best-selling four- door sedan. If there were a recall, there is a probability of 0.18 of a defect in the brake system, 0.17 of a defect in the transmission, 0.25 of a defect in the fuel system, and 0.40 of a defect in some other area. i) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.15? ii) What is the probability that there are no defects in either the brakes or the fueling system? b) if two fair dice are thrown, what is the probability of getting? i) ii) A double six A sum of 8 or more dots

6.) The National Spinal Cord Injury Statistical Center reports that 45% of all spinal cord injuries are caused by vehicle crashes. Suppose that we choose 15 spinal cord injuries at random.a.) What is the probability that 8 of the chosen injuries are from vehicle crashes? (Usethe formula)b.) What is the probability that fewer than 5 of the chosen injuries are from vehiclecrashes? (Use the calculator)c.) What is the probability that more than 9 of the chosen injuries are from vehiclecrashes? (Use the calculator)d.) What is the probability that between 4 and 10 of the chosen injuries are from vehiclecrashes? (Use the calculator)e.) What is the expected number of such injuries to result from vehicle crashes?f.) What is the standard deviation of the number of injuries resulting from vehiclecrashes?

Suppose that 30 percent of an adult population have an infectious disease and 40 percent have achronic disease. Assume that having an infectious disease is independent from having a chronicdisease. For each of the questions below perform the calculation using appropriate statisticalnotation.a. What is the probability that a person selected at random will have both diseases?b. What is the probability of having the infectious disease for people with the chronic disease?c. What is the probability of having the infectious disease for people without the chronic disease?d. What is the probability of not having the infectious disease for people with the chronicdisease?

3. The latest data from the CDC indicates that 14% of Americans are smokers. A researcher wants to identify smokers for a survey. He randomly selects people entering a grocery store to ask if they are a smoker. a) What is the probability that he identifies the first smoker on his 5th try? b) What is the probability that he has to approach more than 8 people before finding the first smoker? c) How many people does he expect to approach before finding the first smoker?