Assume that chocolate chips are distributed within a cake according to a Poisson process with parameter . A cake is divided into two parts of

Assume that chocolate chips are distributed within a cake according to a Poisson process with parameter λ. A cake is divided into two parts of equal volume (disregard the possibility of cutting through a chocolate chip). Show that the probability that each part of the cake has the same number of chips is e−λ∞

k=0

(λ/2)2k

(k!)2 .