Multiple-choice questions each havefive possible answers(a,b,c,d,e), one of which is correct. Assume that you guess the answers to three such questions.

a. Use the multiplication rule to find

P(CWC),

where C denotes a correct answer and W denotes a wrong answer.

P(CWC)=enter your response here

(Type an exactanswer.)

b. ______

c. ______

The following is an example of what I am looking for.

Multiple-choice questions each havefour possible answers(a,b,c,d), one of which is correct. Assume that you guess the answers to three such questions.

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Part 1

a. Use the multiplication rule to findP(CCW), where C denotes a correct answer and W denotes a wrong answer.By the multiplicationrule, since each question is independent of theothers,P(CCW) is equal toP(C)P(C)P(W).

Part 2

If eachmultiple-choice question hasfour possibleanswers, then the probability of guessing the correct answer is14 or0.25.

Part 3

The probability of guessing a wrong answer is34 or

0.75.

Part 4

Now substitute the probabilities into the new expression for

P(CCW) and simplify.

P(CCW)	=	P(C)P(C)P(W)
	=	(0.25)(0.25)(0.75)	=	0.046875

Part 5

b. Beginning withCCW, make a complete list of the different possible arrangements oftwo correctanswers andone wronganswer, then find the probability for each entry in the list.

The easiest way to determine the different possible arrangements is to place the onewrong answer in each possible position and then fill in the other positions. Doingthis, we see that the possible arrangements areCCW,CWC, andWCC.

Part 6

Now find the probabilities forCWC, andWCC.

To doso, follow the same process as in part a.

P(CWC)	=	P(C)P(W)P(C)
	=	(0.25)(0.75)(0.25)	=	0.046875

Part 7

P(WCC)	=	P(W)P(C)P(C)
	=	(0.75)(0.25)(0.25)	=	0.046875

Part 8

c. Based on the precedingresults, what is the probability of getting exactlytwo correct

answers when three guesses aremade?

To find thisanswer, first determine what expression this probability is equal to. Note that the probability of getting exactlytwo correctanswers can be written asP(CCWCWCWCC).

Since the three arrangements aredisjoint, this probability is equal toP(CCW)+P(CWC)+P(WCC).

Part 9

Now substitute in the probabilities and simplify.

P(CCW)+P(CWC)+P(WCC)	=	0.046875+0.046875+0.046875
	=	0.140625

Part 10

Therefore, the probability of getting exactlytwo correctanswers when three guesses are made is

0.140625