A person takes a multiple-choice exam in which each question has four possible a

Question

A person takes a multiple-choice exam in which each question
has four possible answers. Suppose that the person has
no idea about the answers to three of the questions and simply
chooses randomly for each one.
a. What is the probability that the person will answer all
three questions correctly?
b. What is the probability that the person will answer
exactly two questions correctly?
c. What is the probability that the person will answer
exactly one question correctly?
d. What is the probability that the person will answer no
questions correctly?
e. Suppose that the person gets one point of credit for each
correct answer and that 1/3 point is deducted for each
incorrect answer. What is the expected value of the person’s
score for the three questions?

Explanation / Answer

Probability of correct answer = p =1/4

Probability incorrect=1-p=3/4

1) Reuired probability = 1/4*1/4*1/4=1/64

2)Probability of answer 2 correctly of 3 = 3C2 * 1/4*1/4*3/4 = 9/64

3)Probability of answer 1 correctly of 3 = 3C1 * 1/4*3/4*3/4 = 27/64

4) P(No correct ) = 3/4*3/4*3/4 = 27/64

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