All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Matching Matchbox Muse (Posted on 2010-03-30)
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?

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(5): Corrected Solution after Charlie's comments | Comment 14 of 15 |

Sorry, but you have misunderstood the statement of the problem- clearly, as you pointed out, there are trials in which a box containing one match is not selected first by the professor, who instead may choose for say 3 consecutive rounds the other box. But all those cases are not to be counted because the wording of the problem says :

"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? "

meaning that our problem begins if and when the above eventuality has happened, and we are to compute the conditional probability, given the situation that the professor has first chosen the box with the single match

 Posted by Dan Rosen on 2010-07-20 14:37:31
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information