MathDB

A coastal battery sights an enemy cruiser lying one kilometer off the coast and opens fire on it at the rate of one round per minute. After the first shot, the cruiser begins to move away at a speed of

60

kilometers an hour. Let the probability of a hit be 0.75x^{ \minus{} 2}, where

x

denotes the distance (in kilometers) between the cruiser and the coast (

x\geq 1

), and suppose that the battery goes on firing till the cruiser either sinks or disappears. Further, let the probability of the cruiser sinking after

n

hits be 1 \minus{} \frac {1}{4^n} ( n \equal{} 0,1,...). Show that the probability of the cruiser escaping is

\frac {2\sqrt {2}}{3\pi}

Problem Statement