On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses, what is the student's expected gain or loss on the question? Suppose you were using an

1 / 16

Step-by-step explanation:

Number of options = 4

Number of correct answers = 1

Number points gained for a correct answer = 1

Number of points lost for an incorrect answer = 1/4 = 0.25

Probability of choosing a correct option = 1/4

Probability of choosing an incorrect option = 3/4

x 1 - 1/4

P(x) __ 1/4 3/4

Expected gain or loss :

E(x) = Σx*p(x)

E(x) = (1 * 1/4) + (-1/4 * 3/4)

E(x) = 1/4 - 3/16

E(x) = (4 - 3) / 16

E(x) = 1 /16

A gain of 1/16

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step-by-step explanation: