Professor X smokes a pipe. He carries two identical matchboxes, originally containing 20 matches each. When he lights his pipe, he chooses a matchbox at random and lights his pipe with one match and discards the used match.

There will eventually arise an occasion when he first selects a matchbox with only one match in it. At this point, what is the expected number of matches in the other box?

(In reply to re Charlie's solution by Dan Rosen)

"The opening situation, at which point we are asked about the remaining matches, is that in one box is still one match left ( and not zero matches)"

Actually we are not asked about the situation when one box gets down to 1 match. Rather, we're asked about the situation when professor X actually happens to choose that box with one match. When he does so, he reduces the number in that box to zero, and the number remaining in the other box does not change, while it could have been changing during the time that the one box had been reduced to 1, and the time that box is actually selected.

 

Posted by Charlie on 2010-06-29 11:32:14