There are two types of claims that are made to an insurance company. Let Ni (t) denote the number of type i claims made by time t , and suppose that

{N1(t ), t ≥ 0} and {N2(t ), t ≥ 0} are independent Poisson processes with rates

λ1 = 10 and λ2 = 1. The amounts of successive type 1 claims are independent exponential random variables with mean $1000 whereas the amounts from type 2 claims are independent exponential random variables with mean $5000.

A claim for $4000 has just been received; what is the probability it is a type 1 claim?