4. A company manufactures model rockets that require igniters to launch. Once an igniter is used to launch a rocket. the igniter cannot be reused. Sometimes an igniter fails to operate correctly. and the rocket does not launch. The company estimates that the overall failure rate. deï¬ned as the percent of all igniters that fail to operate correctly. is 15 percent. A company engineer develops a new ignitcr. called the super igniter. with the intent of lowering the failure rate. To test the performance of the super igniters, the engineer uses the following process. Step 1: One super igniter is selected at random and used in a rocket. Step 2: If the rocket launches. another super ignites is selected at random and used in a rocket. Step 2 is repeated until the process stops. The process stops when a super igniter fails to operate correctly or 32 super igniters have successfully launched rockets. whichever comes ï¬rst. Assume that super igniter failures are independent. (3) If the failure rate of the super igniters is 15 percent, what is the probability that the ï¬rst 30 super igniters selected using the testing process successfully launch rockets? (b) Given that the ï¬rst 30 super igniters successfully launch rockets. what is the probability that the ï¬rst failure occurs on the thirty-ï¬rst or the thirty-second super igniter tested if the failure rate of the super igniters is 15 percent? (c) Given that the ï¬rst 30 super igniters successfully launch rockets. is it reasonable to believe that the failure rate of the super igniters is less than 15 percent? Explain.
