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Analysis of a situation utilizing the binomial probability distribution.
Natural gas leak detection systems are designed to detect and warn of natural gas leaking from the
cylinder. A reliability question is whether a detection system will be able to identify leaks and issue a
warning. Assume that a particular detection system has a .90 probability of detecting a leak. A statistician
used the binomial probability distribution to answer the following questions, obtaining the answers shown.
Question 1: What is the probability that a single detection system will detect a leak? Answer: 90%
Question 2: If two detection systems are installed and operated independently, what is the probability that
at least one of the systems will detect a leak? Answer: 99%
Question 3: If three detection systems are installed and operated independently, what is the probability
that at least one of the systems will detect a leak?
sample Solution
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