(C ) P C Robot / Test human PC Robot A test human - P ( test human ) P ( test human = 5 100 x 2 + 97 100 100 X 98 100 10 + 9506 = 95 16. 100 00 10000 actually P ( Robot ( Test human ) = 3 100 X 98 29 ! 100 1000 0 291 10ooo 291 9 SIG 10000 9516(b ) p ( actually on test a Robot Robot P( actually a Robot on test Robot P ( on Test Robot p ( actuallay a Robot n on Test 95 Robot 100 PI on Test Robot 484. 10000 Therefore 95 100 95 100-02 I'm not X sure 484 too 454 100 00 my way i's correct P actually actually or not . Test P Robot Test Robot Robot Robot P ( Test Robot ) 95 ? Too X 2 100 484 100 00 190 484in fact Robot Robot. 95 100 in fact Robot / population Not Robot 5 100 in fact Not Robot Not. Robot 100 Not. Robot / Population 98 in fact OC Robot 100 ( a ) P ( Robot ) in fact Robot) + P C Robot) in fact Not Robt =itRobot IT 95 X 2 + 198 100 100 100 X 100 190 + 294 10ooo 484 100 00The 1982 (original) movie Blade Runner (starring Harrison Ford) is set in a future world where there are robots that are designed to look and behave exactly like human beings. The only way to tell if a randomly selected individual (who appears to be human) is in fact a human being or a robot is to administer a test. In our version of the test, suppose that if an individual taking the test is in fact a robot, the test will report that the individual is a robot 95% of the time. If an individual taking the test is not a robot, the test will report that the individual is a robot 3% of the time. Based on the number of robots manufactured, we can estimate that about 2% of all individuals we would test are actually robots. a) (4pts) What is the probability that a randomly selected individual given the test will be classied as a robot? b) (4pts) Given that an individual is classied as a robot by the test, what is the probability that individual is actually a robot? 0) (4pts) Given that an individual is classied as a human by the test, what is the probability that individual is actually a robot