59. 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?