Minus' Solution to

Chair Odds
Posted April 28 - May 4, 1997

There will be 6 chairs left, and 7 children to fill them. 1 child of the 7 will be left chairless. Fox has a 1 in 7 chance of not getting a chair, and a 6 in 7 chance of getting one.

Your Solutions

Andrew MacKinlay [andmak@cygnus.uwa.edu.au] cooked up this delectable dish for Minus' meal. Bravo, Andrew, for impressing our fickle mascot.

Since Amy is assured of getting a chair, we can eliminate her and her chair from the sample. So there are 6 chairs for the remaining 7 people. 1 in 7 people won't get a seat. So, Fox has a 1 in 7 chance of not getting a seat. Therefore, he must have a 6 in 7 chance of getting a seat.

Subajan Sivandran [mai@fir.scotch.wa.edu.au], another Australian chef, shows us that probability can also be expressed as a percentage.

We know that Amy will get a chair, leaving 7 children and 6 chairs. Assuming that all the remaining children have the same chance of getting a chair, then the chances of Fox not getting a chair will be 1 in 7.

Therefore Fox will have a 6 in 7, or 85.7%, chance of getting a chair.

Martin's [joginy99@mail.edu.au] gourmet offering explains why the ratio is calculated out of 7 instead of 8.

Fox has a 85.7% reocurring chance of succeeding.
Amy will definitely get a chair so 6 chairs and 7 kids can be taken into account instead of 7 chairs, 8 kids.
Chance of Fox getting a chair = (kids/chairs) = 6/7 = 85.714%

Heritage Elementary School in Manitoba delighted our mascot with their short and sweet solution. The perfect dessert for a shark with a sweet-tooth.

If there are seven chairs and eight kids then the chances of getting a chair would be 7/8 but if Amy is the fastest and is guaranteed a chair, then the chances are narrowed down to 6/7 (seven kids/six chairs).

These two chefs teased Minus with an answer to the question, but didn't explain how they cooked it up.

Paul Levi [paullevi@vianet.net.au]

Chris Spotts [rfusca@hotmail.com]

Minus had quite an international
feast this week. Australian, Canadian,
and American cuisine. Are there any
European chefs out there?
Minus adores Italian food...