Question

Multiple-choice questions each have four possible answers left parenthesis a comma b comma c comma d right parenthesis​, one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find ​P(CWW​), where C denotes a correct answer and W denotes a wrong answer. ​P(CWW​)equals nothing ​(Type an exact​ answer.) b. Beginning with CWW​, make a complete list of the different possible arrangements of one correct answer and two wrong answers​, then find the probability for each entry in the list. ​P(CWW​)minussee above ​P(WWC​)equals nothing ​P(WCW​)equals nothing ​(Type exact​ answers.) c. Based on the preceding​ results, what is the probability of getting exactly one correct answer when three guesses are​ made? nothing ​(Type an exact​ answer.)

Answer 1

Solution:

Given: Multiple-choice questions each have four possible answers, one of which is correct.

Let   C = Correct Answer and W = Wrong Answer

Thus P(C) = 1/4 = 0.25 and P(W) = 3/4 = 0.75

Assume that you guess the answers to three such questions.

Part a) Use the multiplication rule to find ​P(CWW​), where C denotes a correct answer and W denotes a wrong answer. ​

P(CWW​) = ........?

Since questions are independent, we can write:

P( CWW) = P(C) X P(W) X P(W)

P( CWW) = 0.25 X 0.75 X 0.75

P( CWW) = 0.140625

Part b) Beginning with CWW​, make a complete list of the different possible arrangements of one correct answer and two wrong answers​, then find the probability for each entry in the list. ​

List of one correct answer and two wrong answers​:

{ CWW , WWC , WCW }

P( CWW) = P(C) X P(W) X P(W)

P( CWW) = 0.25 X 0.75 X 0.75

P( CWW) = 0.140625

P( WWC ) =P(W) X P(W) X P(C)

P( WWC ) = 0.75 X 0.75 X 0.25

P( WWC ) = 0.140625

P( WCW ) =P(W) X P(C) X P(W)

P( WCW ) = 0..75 X 0.25 X 0.75

P( WCW ) = 0.140625

Part c. Based on the preceding​ results, what is the probability of getting exactly one correct answer when three guesses are​ made?

P( getting exactly one correct answer when three guesses are​ made) = .......?

P( getting exactly one correct answer when three guesses are​ made) = P( CWW) + P( WWC ) + P( WCW )

P( getting exactly one correct answer when three guesses are​ made) = 0.140625 +0.140625 +0.140625

P( getting exactly one correct answer when three guesses are​ made) = 0.421875