a A person takes a multiple choice exam in which each questi

a) 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.

Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deduced for each incorrect answer. What is the expected value of the person’s score for the three questions?

b) A person pays $1 to play the following game: The person tosses a fair coin 4 times. If no heads occur, the person pays an additional $2, if one head occurs, the person pays an additional $1, if two heads occur, the person just loses the initial dollar, if three heads occur, the person wins $3, and if four heads occur, the person wins $4. What is the person’s expected gain or loss?

Solution

a)

Expected value = 3 * (1/4 *1 - 3/4*1/3) = 0 Answer

b)

P(No head) = 1/16
P(1 head) = 4/16 = 1/4
P(2 Head) = 6/16 = 3/8
P(3 Head) = 4/16 =1/4
P(4 Heads) = 1/16

Expected value = 1/16*(-2) + 1/4*(-1) + 3/8*(-1) + 1/4*(3) + 1/16*(4) = 0.25 Answer

Gain