Joe takes part in math competitions. a particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. it awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. joe is sure of 12 of his answers. he ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. what is his expected score?
a) 69.2
b) 90.8
c) 97.2

solution:

total number of question in the competition= 25

marks for each correct answer= 6 points

marks for question left blank= 1.5

marks for incorrect answers=0

number of correct answers by joe= 12

so, marks obtained for correct answers= 12 × 6=72

as, joe guessed   4 of the other questions and randomly guessed on the 9 remaining problems.

so, we are not sure whether how many questions joe has done correctly or incorrectly.

but points awarded for correct as well as incorrect answer is multiple of 0.5.

so, total marks obtained must be also multiple of 0.5.

so, none of the option from (a) to (c) is true.

90.8 is the answer, i guessed and got it correct