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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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 re(2): Debugged! (spoiler) | Comment 3 of 5 |
(In reply to re: Debugged! (spoiler) by JayDeeKay)

That's how I read Steve's solution;

"within 3 trials" includes 1, 2, or 3.

(1/24) + (23/24)*(1/23) + (22/24)*(1/22) = 3/24 = 1/8

That's 1/24 probability it's found on the first trial
plus the (*23/24)*(1/23) probability that it's not found on the first trial but is found on the second; plus the probability that it's found on neither the first nor the second trial but is found on the third.

 Posted by Charlie on 2018-04-16 21:11:39

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