Final answer:
The expected final score for guessing on a 25-question multiple choice quiz, where each correct answer awards 4 points, is 25 points.
Step-by-step explanation:
To calculate the expected score when guessing on a multiple-choice quiz with 25 questions, where each correct answer is worth 4 points and each incorrect answer is 0 points, we will use the concept of probability. Since there are 4 possible answers for each question and only 1 correct answer, the probability of guessing the correct answer is 1/4, and the probability of guessing wrong is 3/4.
To find the expected score, we multiply the probability of a correct answer by the points awarded for a correct answer and then multiply by the total number of questions:
Expected score = Probability of correct answer × Points per correct answer × Total number of questions
Expected score = (1/4) × 4 points × 25 questions
In this case, because a correct answer awards 4 points, and every question guessed correctly has a 1/4 chance:
Expected score = 1 × 25 = 25 points
Therefore, if a student guesses on all questions, they can expect to earn an average final score of 25 points on this quiz.