The Department of Transportation’s National Highway Traffic Safety Administration has the authority to require manufacturers to recall vehicles that have safety-related defects or do not meet Federal safety standards. Assume that the time between major safety recalls follows an exponential distribution, and on average a major recall occurs 6 times in a decade.
Part A: What is the probability that less than three months will pass before the next major safety recall?
Part B: Given that no major safety recall occurs within the next 9 months, what is the probability that it will occur within a year?
Part C: What is the probability that a major safety recall will occur between three and four years from now?