Harry, a dog owner went on a walk with his dog to a Hike Trail and accidentally lost his dog. Suppose the dog is lost in the Hike Trail, and the police has decided to apply 'Bayesian Probability Techniques' to aid their search. The trail is divided into two distinct districts, A and B. Based on the dog's known itinerary, it is estimated that the dog is twice as likely to be in district A as district B. Due to the differing difficulty of the terrain in each district, a helicopter search of district A is estimated to have 60% chance of success, and of district B an 80% chance of success. You must define all terms and notation in depth and show thorough details of your calculations. iv. What is the probability that the dog is in District B? What is the probability that the dog is found after only searching District A? If District A is searched and the dog is not found, what is the probability that the dog is in District B? What is the probability that the dog is not found after a search of both districts? (Here, assume it is a simultaneous search of both districts). Suppose the entire Hike Trail is searched, and the dog is not found, what is the probability that the dog is in District B