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. 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.

(b) write the following event in set notation.
the student gets four answers wrong.
{ wwwww } (use a comma to separate answers as needed.)

(c) write the following event in set notation.
the student gets exactly three answers correct.
(use a comma to separate answers as needed )

Explanation:

Part (c)

Step1: Define correct and wrong

Let \( c \) represent a correct answer and \( w \) represent a wrong answer. We need exactly 3 correct and 1 wrong.

Step2: List all permutations

The possible combinations (permutations) of 3 correct (\( c \)) and 1 wrong (\( w \)) in 4 questions are: \( cc cw \), \( cc wc \), \( cw cc \), \( w cc c \). So in set notation, we list each of these.

Answer:

\(\{cccw, ccwc, cwcc, wccc\}\)