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A Southwest Energy Company pipeline has 3 safety shutoff valves in case the line springs a...

A Southwest Energy Company pipeline has 3 safety shutoff valves in case the line springs a leak. These valves are designed to operate independently of one another. There is only a 7% chance that valve 1 will fail at any one time, a 10% failure chance for valve 2, and a 5% failure chance for valve 3. If there is a leak, find the following probabilities:

  1. that all 3 valves operate correctly.
  2. that all three valves fail.
  3. that at least one valve operates correctly.
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