You are given a 100*50 snooker table (felt area) and two balls of diameter 1. One ball is placed in the center of the table and the other ball is randomly positioned. What is the probability that I will be able to shoot this second ball directly into the top left pocket without touching the central ball? (Assume pocket has radius 1)

Assuming no bounces are allowed and no spin can be applied (this is my interpretation of "...shoot the second ball directly into the top left pocket...") and, assuming you are an excellent snooker player.  The probability is about (5000-184)/5000 = .9632, about 96%, that you will be able to do this.

The "fuzzy shadow" produced by a diameter 2 light source positioned in the top left corner of a 50 by 100 table as the light falls on a diameter 1 object in the center of the table, covers an area of approximately 184 square units.  With the term "fuzzy shadow" I am taking into account the clearance required for the shot ball, with a diameter of 1, to pass the fixed ball.

Estimated by ruler and eye on graph paper.

Posted by Mindrod on 2006-02-11 12:12:41