Question

an unprepared student takes a four-question, true/false quiz. the student guesses the answers to all four questions, so each answer is equally likely to be correct or wrong. complete parts (a) through (d) below.
c. ( s = {cccc,wwww} )
d. ( s = {cccc} )
( n(s) = 16 )
(type a whole number.)
are the outcomes in ( s ) equally likely?
a. yes. since the student studied for the test, the likelihood the student gets the answer correct is the same as the likelihood the student gets it wrong.
b. no. because the student studied for the test, the likelihood that the student gets more answers correct is higher than the likelihood that the student gets more answers wrong.
c. no. because the student guesses on each of the questions, the likelihood the student gets the answer correct is not the same as the likelihood the student gets it wrong.
d. yes. because the student guesses on each of the questions, the likelihood the student gets the answer correct is the same as the likelihood the student gets it wrong.

Explanation:

The student is guessing on a true/false quiz, so for each question, the probability of being correct (c) or wrong (w) is equal (each has a probability of $\frac{1}{2}$). When guessing, the likelihood of correct and wrong answers for each question is the same, and this extends to the outcomes in the sample space \( S \) (all possible sequences of correct/wrong for 4 questions). Option A is incorrect as the student is unprepared (didn't study). Option B is incorrect because guessing means equal chance for correct/wrong, not a higher chance for correct. Option C is incorrect as guessing on true/false gives equal likelihood for correct and wrong. Option D correctly states that since the student guesses, the likelihood of correct and wrong answers is the same, so outcomes in \( S \) are equally likely.

Answer:

D. Yes. Because the student guesses on each of the questions, the likelihood the student gets the answer correct is the same as the likelihood the student gets it wrong.