Re: Statistics

[Dung Trong Nguyen <nguyen@jaist.ac.jp>]

Dang Hung Thang <thang@mathematik.uni-Bremen.de> wrote:

>   Thu+a tha^`y va^~n la` 2/3 tho^i a !
> You are right. Can you explain why ?

The probability must still be 2/3 as A's question seems to unveil no
information about the case of himself. We carry out a formally
calculation. The released couple can be either AB, BC or CA, so P(AB)
= 1/3.  The answer of A's question can be either B or C, so P(answer =
B) = 1/2.  We have

	P(A/answer = B) = P(AB) / P(answer = B) = 1/3 / 1/2 = 2/3

The calculation gives us exactly the number as our intuitive guess
does.  Therefore there no pradox here at all.

To see a paradox as tha^`y Tha('ng has promised, we change the
condition a little.  The names of two lucky guys then are written down
in two folded pieces of paper.  As it happened A picked up one of
them, and saw B's name inside.  So now what is A's chance?

Just again do some caculation. The probability of "A pick B's name" is
2/3 x 1/2 = 1/3 as we expected, then

	P(A/A pick B) = P(AB) / P(A pick B) = 1/3 / 1/3 = 1 

Do you think A surely can see his wife next day ? :))

Dang Hung Thang <thang@mathematik.uni-Bremen.de> wrote:

> Co' mo^.t paradox sau dda^y elementery but interesting.  Ba tu`
> nha^n A,B va` C co' tha`nh ti'ch ca?i ta.o nhu+ nhau. Ho. du+o+c
> bie^'t nha^n nga`y Quo^'c kha'ch co' 2 ngu+o+`i se~ ddu+o+.c th?a. A
> nghi~ ra(`ng nhu+ va^.y xa'c sua^'t dde^? mi`nh ddu+o+.c tha? la`
> 2/3.  A ho?i do` mo^.t ngu+o+`i o+? to`a a'n xin cho bie^'t te^n
> cu?a mo^.t ngu+o+`i ddu+o.c tha? kha'c A ( A kho^ng da'm ho?i
> tha(?ng ve^` mi`nh).Ngu+o+`i ddo' tra? lo+`i la` B ddu+o+.c tha?. A
> hoa?ng qua' vi` ba^y gio+` XS ddu+o+. tha? cu?a mi`nh chi? co`n 1/2.
> Va^.y XS ddu+o+c tha? cua? A la` bao nhie^u?