# Statistics puzzle i05244c

Warren Gallin wgallin at gpu.srv.ualberta.ca
Tue Jun 14 11:29:33 EST 1994

```In Article <2tfv1n\$t8d at cville-srv.wam.umd.edu>, bcohen at wam.umd.edu (Brad
Cohen) wrote:
>
>Martin Gardner says that new mathematical puzzles are very
>difficult to devise.  What do you think of this one?
>
>A slightly less-than-honest bridge player (south) caught a
>glimpse of a card dealt to her opponent on the left (west) - it
>was a red ace (she could not tell which suit).  This opponent --
>west -- opens the game by playing the ace of diamonds.  South
>sees that neither she nor the revealed cards of north have the
>ace of hearts, which must be in either east's hand or west's
>hand.  What is the probability now that west has the ace of
>hearts?

>For a solution using the resampling method, contact pcbruce at wam.umd.edu)

Here's an unsophisticated answer; is there anything wrong with it?

The odds should be 50:50, assuming that we are talking about the first trick
being completely played.  All south knows is that she saw a red ace, and a
red ace has been played.  Therefore the chances of east and west having the
ace of hearts should be equal.
Warren Gallin,
Department of Zoology, University of Alberta
wgallin at gpu.srv.ualberta.ca

```