2 points Save Answer This bonus problem uses both Bayes' Rule and Poisson probability distributions. Suppose that in a certain mythical adventure game, at random times during play, a dragon will arrive in the player's vicinity, flying down from the sky. More dragons appear at higher difficulty levels; the following chart gives the average dragon arrival rates: Average dragon arrival Selected game difficulty rate (per hour of game time) Easy 0.4 Medium 0.8 Hard 1.6 Nightmare 2.5 Assume that, given a certain difficulty, the number of dragons that appear during an interval of game time t follows a Poisson distribution. Suppose you are watching a friend play but do not know the selected difficulty and want to try and guess. During an hour of play, your friend encounters the arrival of a whopping 4 dragons. That's a lot of dragons for one hour. You suppose your friend has chosen the Nightmare difficulty; what is the probability you are correct? Use Bayes' Rule. Assume an equal initial probability of 1/4 for each difficulty. Give the probability in decimal form to four places