Question

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?○ 69.2○ 75.6○ 90.8○ 97.2

Explanation:

Step1: Calculate points for sure answers

Points = $12 \times 6 = 72$

Step2: Calculate expected points for 4 guessed questions (3 choices left)

Probability of correct guess: $\frac{1}{3}$
Expected points per question = $6 \times \frac{1}{3} + 0 \times \frac{2}{3} = 2$
Total for 4 questions: $4 \times 2 = 8$

Step3: Calculate expected points for 9 guessed questions (5 choices)

Probability of correct guess: $\frac{1}{5}$
Expected points per question = $6 \times \frac{1}{5} + 0 \times \frac{4}{5} = 1.2$
Total for 9 questions: $9 \times 1.2 = 10.8$

Step4: Sum all expected points

Total expected score = $72 + 8 + 10.8$

Answer:

90.8