A test contains six questions. In each question the student has to choose one of two possible answers. Each correct answer yields one point. 2/ 3 of the participants are hard-working and the remaining ones are lazy. A hardworking student answers each question correctly with probability 0.9, independent of the other questions. A lazy student chooses each answer uni- formly at random from the two choices and gets it right with probability 0.5. a.) If a student is hardworking, what is the probability that the person gets exactly 3 points? b.) If a student is lazy, what is the probability that the person gets exactly 3 points? c.) If a student gets exactly 3 points, what is the probability that the person is lazy