There are 4 identical boxes filled to the top with marbles. Your friend is playing around with your favorite marble and accidentally drops it into one of the 4 boxes (assuming that all marbles look almost identical). Now it is equally likely that your marble could be in any of the 4 boxes. Using a sorter to try to find your lost marble, the probability of the machine finding your marble from any box, if it is in fact there, is 0.75. How after sorting through the first box, the machine does not turn up your marble. What is the probability that the marble is in box 1, 2, 3, 4?
I understand this problem to be some sort of conditional probability. P(marble being in box i | machine could not find it in box 1).
The Attempt at a Solution
All I can get from this so far is conditional probability. I can see that if the marble was in fact in box 1, there is a 25% chance that the machine just couldn't find it because of its own error and that remains the same for all 4 boxes.