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)

See my last post for definitions.

Here are some approximations:
The  left  near miss point is (24.016, 50.447)
The right near miss point is (25,894, 49.553)

Some approximate equations:
Line AE: Y = 2.051 X + 1  (thru (0,1) and the left nmp
Line BC: Y = 1.991 X - 1.991  (thru (1,0) and right nmp
Line AB: Y = -0.5 X + 62.5  (connects the two nmp's)
Line CD:  X=50  (vertical line)
Line DE:   Y = 100 (horizontal line)

The area between all these lines is the pentagon ABCDE.

But that only counts half of the diameter 2 circle at the center of the table, so add another pi/2 to the area of ABCDE.

Posted by Larry on 2006-02-12 09:58:28