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 Debugging a system (Posted on 2018-04-16)
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 No Rating

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 Debugged! (spoiler) | Comment 1 of 5
Not sure why this is Difficulty 3.  I did it in seconds in my head.

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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