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?

Respuesta :

Considering the probabilities of getting each question right, his expected score for the test is 90.8.

How to find Joe's expected score?

Joe's expected score is given by the sum of the expected score for each question.

We have that:

  • He is sure of 12 answers, hence for each he expects 6 points.
  • He randomly guesses on 9 problems, hence he is expected to have a 1/5 probability of earning 6 on them.
  • For the other 4 problems, he has a 1/3 probability of earning 6 on them, as he will guess from 3 options as he eliminated 2.

Hence his expected score is given by:

E(X) = 12 x 6 + 9 x 1/5 x 6 + 4 x 1/3 x 6 = 90.8.

More can be learned about the expected score of a distribution at https://brainly.com/question/13617733

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