Question

Each question on a multiple-choice exam has five choices. One of the choices is the correct answer, worth 7 points, another choice is wrong but still carries partial credit of 4 points, and the other three choices are worth 0 points. If a student picks answers at random, what is the expected value of his or her score for a problem? points If the exam has 20 questions, what is his or her expected score? points

Answer 1

Answer:

Given,

Here there are 5 choices for each question.

One of the choice is absolute correct & carries 7

P(Getting 7) = 1/5 = 0.2

P(Getting 4) = 1/5 = 0.2

Remaining 3 chances, 0 points = 3/5 = 0.6

Expected score = x*P(x)

= 7*0.2 + 4*0.2 + 0*0.6

= 1.4 + 0.8 + 0

= 2.2

No. of questions = 20

Expected score = 20*2.2

= 44