Question

A true-false test consists of 30 questions.

a) If a student is merely guessing, what is the expected value of the number of correct responses?
b) If a student just randomly guesses on each of the 30 questions, what is the expected value of correct responses?

Answer 1

a) The expected value of the number of correct responses for a true-false test is 15. b) If a student randomly guesses on each question, the expected value is still 15.

Step-by-step explanation:

a) The expected value of the number of correct responses for a true-false test can be found by multiplying the probability of getting each question correct (1/2 in this case) by the total number of questions. So, the expected value for a 30-question test would be: 30 x (1/2) = 15.

b) If a student randomly guesses on each of the 30 questions, the probability of getting each question correct is still 1/2. Therefore, the expected value for the number of correct responses would be the same as in part a: 15.