Poisson Processes and Bayes' Rule

Question

We observe a Poisson process with unknown rate. The rate 𝜆 of the Poisson process is either 2 or 4, with equal probability, and the actual value is not known. We observe the process over the time interval [0,3] and observe exactly 9 arrivals. Given this information, determine the conditional probability that 𝜆=2 .

Answer 1

.4408