Logic Question

[thylacine]

First, I'll assume that this isn't actually a logic question since it is posted in the probability forum. I'll also assume that claims of this type are always true, and also that there are no ties in the international buffet rankings. Furthermore, I will assume that all buffets in the world post a truthful sign outside saying, for some positive integer j, that they are rated one the top j buffets in the world. This will imply with certainty that they are in fact rated exactly i^th in the world for some positive integer i that is less than or equal to j.

Now for the detailed calculation. For positive integers i and j, suppose that P(i,j) is the probability that a buffet that is actually rated exactly i^th in the world, will post a sign outside saying that they rated one the top j buffets in the world. So of course P(i,j)=0 whenever j is less than i, and

\Sum_{j=i}^{\infty} P(i,j)=1.

Then the probability that a buffet claiming to be rated one the top j buffets in the world, is actually rated exactly i^th in the world is

P(i,j)/ [ \Sum_{k=1}^{j} P(k,j) ].

I may have intentionally made a mistake in what I just wrote. I'm not sure. You guys don't need to be going to buffets anyway.

[Mason Malmuth]

2[img]/images/graemlins/diamond.gif[/img] + 2[img]/images/graemlins/club.gif[/img] = 4[img]/images/graemlins/heart.gif[/img]

MM

[kleraudio]

was that a joke mr. malmuth. an advertisement for the books comin out perhaps? or are you serious?

Jim [img]/images/graemlins/spade.gif[/img]

[submariner]

#5. Otherwise they would have said one of the top 4, top 3, etc.

[Trix]

top4 sounds lame, same with top2. So it´s either number 2,4 or 5.

[Warren Whitmore]

I am going to go with 8500th. Its a big world after all with a lot of buffet's in it. I may not be right but I have got to be closer than 5.

"Its better to be vaguly right than precisly wrong"
John Maynard Keynes

[AngryCola]

Hi Mason,

That is just plain sick! [img]/images/graemlins/grin.gif[/img] [img]/images/graemlins/spade.gif[/img]

[flair1239]

It is rated 5th. If it had been rated higher, then they would have said something like: "Rated one of the top 3".

[elwoodblues]

It has to be 5 or 4. You wouldn't say "one of the top 4," just doesn't have a ring to it. 3 or 2 would be in the "top 3" (you wouldn't say 2nd best buffet) and 1 would be "the number 1 buffet."

[Beerfund]

Never have I ever seen a thread with more of the same exact answers before.......uhhhh it has to be 4 or 5 because they wouldnt say we're 1 of 5 if they were #3 blahblahblahhhhhhhh [img]/images/graemlins/mad.gif[/img]