There are 4 identical boxes filled to the top with marbles. Yourfriend is playin
ID: 2913883 • Letter: T
Question
There are 4 identical boxes filled to the top with marbles. Yourfriend is playing around with your favorite marble and accidentallydrops it into one of the 4 boxes (assuming that all marbles lookalmost identical). Now it is equally likely that your marble couldbe in any of the 4 boxes. Using a sorter to try to find your lostmarble, the probability of the machine finding your marble from anybox, if it is in fact there, is 0.75. How after sorting through thefirst box, the machine does not turn up your marble. What is theprobability that the marble is in box 1, 2, 3, 4?I understand this problem to be some sort of conditionalprobability. P(marble being in box i | machine could not find it inbox 1). All I can get from this so far is conditionalprobability.
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 ownerror and that remains the same for all 4 boxes. Please help.
Explanation / Answer
Before sorting the first box the P was .25. Multiplythis by .25 (which is 1 - .75, the P that the marble wasthere but missed) gives you an new probability of .0625. Thisincreases the P that it fell into another box. Imaginethat the sorter was perfect. The p of box 1 would be 0so the P of the other boxes must be .333. As it was notperfect, the P of the each other box is (1-(.25)*(1-.75))/3 or.3125. I hope that is clear. Try playing around with the P ofthe sorter and imagine the out comes. As P-> 1 the P ofthe other boxes -> .333. As P->0, the P of the otherboxes remains at .25. Good luck!Related Questions
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