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natima [27]
2 years ago
9

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 poss

ible 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?
Mathematics
1 answer:
marshall27 [118]2 years ago
7 0

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

<h3>How to find Joe's expected score?</h3>

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 brainly.com/question/13617733

#SPJ1

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