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An absent-minded professor goes for a walk carrying a digital audio device using 2 batteries. He has 2 fresh replacement batteries stashed away in one of four pockets. Sure enough, both batteries lose their charge and he removes them. Not wanting to throw the depleted batteries into the woods, he places them into a pocket chosen at random from the 4 available. A little while later he remembers the two fresh batteries, but he cannot remember which pocket. He fishes around in his pockets until he finds one with batteries (either 2 or 4 indistinguishable batteries). He removes 2 batteries and inserts them into the digital audio device. The digital audio device requires at least one good battery in order to play. Find the probability the digital audio device works on the first try.

I believe the denominator should be $(4)_2$, but I am having trouble with what the numerator should be.

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    you can choose the batteries so that both of them are dead batteries, and there is only 1 choice for it. so the numerator is $(4)_2$ -12012-03-11
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    Is there a typo in this problem in that the professor has **4** good batteries in one pocket at the start (**not 2** as the problem statement says), and then after a short while and the first replacement and the second failure, we have a situation of either 2 good batteries in one pocket and 2 bad in another or 4 batteries in one pocket of which 2 are good and 2 bad? Else the statement _He has 2 fresh replacement batteries stashed away in one of four pockets._ would imply that after the second failure, he has 4 dead batteries on him.2012-03-11

3 Answers 3