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. (a) write out the sample space s, choosing s with equally likely outcomes, if possible. then give the value of n(s) and tell whether the outcomes in s are equally likely. let c represent a correct answer and let w represent a wrong answer. choose the correct answer below. a. s = {ccc, ccw, cwc, wcc, cww, wcw, wwc, www} b. s = {cccc, cccw, ccwc, cwcc, wccc, ccww, cwcw, wccw, wcwc, wwcc, cwwc, cwww, wcww, wwcw, wwwc, wwww} c. s = {cccc,wwww} d. s = {cccc} n(s) = (type a whole number.)

Explanation:

Step1: Analyze the quiz structure

There are 4 true/false questions, each with 2 possible answers (c or w). The sample space should include all possible sequences of 4 answers.

Step2: Determine the number of outcomes

For each of the 4 questions, there are 2 choices. By the multiplication principle, the total number of outcomes is $2\times2\times2\times2 = 2^4$.

Step3: Calculate $2^4$

$2^4 = 16$. So the number of elements in the sample space \( n(S) \) is 16. Also, option B correctly lists all 16 possible 4 - character sequences of c and w, and each outcome is equally likely since each answer (c or w) has the same probability for each question.

Answer:

16