A recent flooding weakened pipes throughout a municipality A

A recent flooding weakened pipes throughout a municipality. An inspector is assigned the task of checking pipes of public facilities. The inspector will carry a portable kit (on rollers), which has enough material to repair up to three minor leaks. Past experience suggests that the chance of finding a minor leak at any of the sites to be inspected is 20%.

1. What is the chance that the inspector will use up the kit on the 7th inspection? You can use formulas from the text, BUT be careful in deciding what is a Success and what is a Failure. (Give your answer to five decimal places.)

2. What is the chance that the inspector will use up the kit on the 15th inspection? (Give your answer to five decimal places.)

3. What is the expected value for the number of inspections that a single kit will last? (That is, what is E (X ) is X is the number of the last repair that a kit makes.)

4. What is the variance for the number of inspections that a single kit will last? (That is, what is V (X ) is X is the number of the last repair that a kit makes.)

Solution