Originally Posted by

**BrooketheChook** A bee needs to collect pollen for his hive. The positions of flowering flowering gum trees and flowering iron bark trees can be described by a pair of spatial Poisson processes with rates

$\displaystyle \lambda (x,y) = \frac{1 - (\cos(x^2+y^2))^2}{1+\sqrt{(x^2+y^2)}} \ $ and $\displaystyle \ \nu (x,y) = \frac{1 - (\sin(x^2+y^2))^2}{1+\sqrt{(x^2+y^2)}}$

respectively, where $\displaystyle x$ and $\displaystyle y$ are measured in kilometers from the beehive.

Find

(a) the probability that the bee will have to fly more than 1km to reach a flowering tree.