Question

Due to pressing social commitments, a student, was not able to study for an examination. The examination consists of 4 multiple choice questions. Each question has 6 possible answers from which to choose, only one of which is correct. The student plans to answer the questions randomly by rolling a fair die for each question and choosing the response associated with the number rolled. Let X denote the number of questions correctly answered by the student.

a)      What is the probability mass function for the random variable X?

b)      If the professor assigns a credit of ten points for every correct answer and deducts one point for every incorrect answer, what is the student’s expected score?

c)       The professor deducts points for wrong answers in order to discourage random guessing. If 10 points are credited for each correct answer, how many points should be deducted for each wrong answer so that the student’s expected score from guessing is zero?

Answer 1