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.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
Transcribed Image Text: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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