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)
(In reply to Solution
I overlooked the fact that the second ball cannot be placed closer than 0.5 units from the edge of the table. This reduces the effective area of the table to 49*99 - 3.2 = 4847.8 sq. units. It also reduces the area of the "forbidden zone" by about 4 sq. units along the lower right edges of the table, to 237.6 sq. units.
The revised probability of randomly placing the second ball outside of the "forbidden zone" is approximately:
P = (4847.8 - 237.6)/4847.8 = .951, or 95.1%
Posted by Mindrod
on 2006-02-13 09:54:12