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Debugging a system (Posted on 2018-04-16) Difficulty: 3 of 5
A certain device consists of 24 equally reliable components. It is known that one (and only one) is faulty. The location of the failed component is performed by replacement - one after another.

1. Find the probabilty of restoring the functioning of the system within 3 trials.
2. Same question for n trials.

See The Solution Submitted by Ady TZIDON    
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Solution Debugged! (spoiler) | Comment 1 of 5
Not sure why this is Difficulty 3.  I did it in seconds in my head.

Answers are 
1) 3/24 = 1/8
2) n/24

If it helps, consider the equivalent problem of replacing n at once.  Obviously, the probability of replacing the defective one is n/24.

Even the slow way of doing it is simple.  Doing it one at a time, the probability (with 3 replacements) =
  (1/24) + (23/24)*(1/23) + (22/24)*(1/22) = 3/24 = 1/8

  Posted by Steve Herman on 2018-04-16 12:23:01
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