The test questions are formed as follows:The questions are in a language you have never seen: a mixture of Navaho, Swahili, Klingon, andEsperanto. So you have to guess on all of the questions and there are no contextual clues toeliminate any answers. This is the first one:'Arlogh Qoylu'pu'?Moja: Yel kholgo eeah.Mbili: Floroj kreskas ĉirkaŭ mia domo. Pe'el!Tatu: La sandviĉo estos manĝota'mo'tlhIngan maH!Nne: 'Adeez'æ`q eeah.(The professor sits at the front of class with a giant, sadistic grin while the studentsthrow wads of paper at his head.)Using the binomial probability rule, the law of total probability and Bayes’ theorem:a)What is the probability of getting two right on each sub-exam? (T1, T2, and T3, separately.)
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b)What are your overall chances of passing the entire exam?
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c)What are your chances of passing T3 if you first pass T1 and T2?
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Problem Hint:Structure your analysis.Figure out the component probabilities: p(passing test 1), p(passing test 2), p(passingtest 3).Make a table of their proportional contributions of probability to the whole.Calculate the total probability: p(Total).Continue using Bayes’ theorem to calculate the probability of passing test 3 conditionalon passing tests 1 and 2.