4. An airplane is missing. Based on its flight plan, it has been determined that the airplane is equally likely to be in any one of three locations (each with probability 1/3). Some locations are easier to search than others for various geological reasons. If the airplane is in location 1,2,3 then the team will find it while searching there with probability 1/2, 1/3, 1/4, respectively. Suppose that location 1 is searched first, and the airplane is not found there. Show that, given this, with conditional probability 2/5 the airplane is in location 2.

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