Multiple-choice questions each

Solution:

Given: Multiple-choice questions each have four possibleanswers, 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 wronganswer. ​

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 completelist of the different possible arrangements of one correct answerand two wrong answers​, then find the probability for each entry inthe 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, whatis the probability of getting exactly one correct answer when threeguesses 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 guessesare​ made) = 0.421875