?Multiple-choice questions each have four possible answers left parenthesis (a,

Question

?Multiple-choice questions each have four possible answers left parenthesis (a, b, c, d)?, one of which is correct. Assume that you guess the answers to three such questions.a. Use the multiplication rule to find ?P(WCC) where C denotes a correct answer and W denotes a wrong answer.

?P(WCC)=

?(Type an exact? answer.)

b. Beginning with

WCC, make a complete list of the different possible arrangements of two correct answers and one wrong answer?,

then find the probability for each entry in the list.

?P(WCC) minus?see above

?P(CCW) =

?P(CWC) =

?(Type exact? answers.)

c. Based on the preceding? results, what is the probability of getting exactly two correct answers when three guesses are? made?

Explanation / Answer

As there are 4 choices to each question, therefore for any question, P(W) = 3/4 = 0.75 and P(C) = 1/4 = 0.25

a) P(WCC) is computed as:

P(WCC) = 0.75*0.252 = 0.046875

b) P(WCC) = 0.046875
P(CCW) = 0.046875
P(CWC) = 0.046875

c) Here, we just add the above computed probabilities as:

probability of getting exactly two correct answers when three guesses are made is computed as:

= 3*0.046875

= 0.140625

Therefore 0.140625 is the required probability here.

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