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A company manufactures model rockets that require igniters to launch. Once an igniter is used to launch a rocket, that 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, defined as the percentage of all igniters that fail to operate correctly, is 15%.

An engineer at the company, develops a new igniter, called the super igniter, with the intent of lowering the failure rate. To test the performance of the super igniters, he 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 igniter is selected at random and used in rocket.

Step two is repeated until the process stops. The process stops when a super igniter fails to operate correctly, or when 32 super igniters have successfully launched rockets, whichever comes first. Assume that super igniter failures are independent.

(a) If the failure rate of the super igniters is 15%, what is the probability that the first 30 super igniters selected using the testing process successfully launch rockets??

(b)Given that the first 30 super igniters successfully launch rockets, what is the probability that the first failure occurs on the 31st or 32nd super igniter tested?

(c) Suppose the first 30 super igniters successfully launch rockets. Does this provide convincing evidence that the failure rate of the super igniters is less than 15%? Justify your answer