Aldrich Ames is a convicted traitor who leaked American secretsto a foreign power. Yet Ames took routine lie detector tests andeach time passed them. How can this be done? Recognizing controlquestions, employing unusual breathing patterns, biting one'stongue at the right time, pressing one's toes hard to the floor,and counting backwards by 7 are countermeasures that are difficultto detect but can change the results of a polygraph examination†.In fact, it is reported in Professor Ford's book that after only 20minutes of instruction by \"Buzz\" Fay (a prison inmate), 85% ofthose trained were able to pass the polygraph examination even whenguilty of a crime. Suppose that a random sample of eleven students(in a psychology laboratory) are told a \"secret\" and then giveninstructions on how to pass the polygraph examination withoutrevealing their knowledge of the secret. What are the followingprobabilities? (Round your answers to three decimal places.)
(a) all the students are able to pass the polygraphexamination
(b) more than half the students are able to pass the polygraphexamination
(c) no more than half of the students are able to pass thepolygraph examination
(d) all the students fail the polygraph examination
