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.
Not sure why this is Difficulty 3. I did it in seconds in my head.
1) 3/24 = 1/8
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