A student was totally unprepared for a multiple-choice test and had to absolutely guess the answer to every one of the 100 questions. About what score (percent) would you expect him to earn if there were four possible answers to every question?
I'm not sure where to start on this one. I know how to find the probability of one letter being the correct answer (1/4) but I do not know how to work through this type of problem.
Thanks
1/4 * 100 = 25
To determine the expected score for this student, you can use the concept of expected value. The expected value represents the average outcome when an experiment is repeated multiple times.
In this case, there are 100 multiple-choice questions, and since the student is guessing, there is a 1/4 (or 25%) chance of choosing the correct answer for each question.
To find the expected value, you can multiply the probability of each outcome (25% or 0.25) by the value of that outcome (1 point for each correct answer). Since all questions have equal weight, the value is always 1.
Next, calculate the expected value using the following formula:
Expected Value = (Probability 1) x (Value 1) + (Probability 2) x (Value 2) + ...
Since each question has the same probability of being answered correctly, the formula simplifies to:
Expected Value = (Probability) x (Value)
Therefore, the expected value for one question is:
Expected Value = 0.25 x 1 = 0.25
Since there are 100 questions, you can multiply the expected value of one question by 100:
Expected Score = 0.25 x 100 = 25
Therefore, you would expect the student to earn a score of approximately 25% on the test if they guessed the answer to all 100 questions.