Multiple-choice questions each have four possible answers (a, b, c, d), one of w

Question

Multiple-choice questions each have four possible answers (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(WWC), where C denotes a correct answer and W denotes a wrong answer. P(WWC) = b. Beginning with WWC, 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(WWC) = see above P(WCW) = P(CWW) = c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

Explanation / Answer

For each question there are 4 possible answers (a,b,c,d). Therefore the probability of the correct answer is P(C) = 1/4 and the probability of the wrong answer is P(W) = 3/4.

(a)

P(WWC) = P(W)*P(W)*P(C) (using the multiplication rule)

= (3/4)*(3/4)*(1/4)

= 9/64

(b)

P(WWC) = 9/64

P(WCW) = (3/4)*(1/4)*(3/4) = 9/64

P(CWW) = (1/4)*(3/4)*(3/4) = 9/64

(c)

Probability of getting exactly one correct answer when 3 guesses are made is,

P(WWC) = P(WCW) = P(CWW) = 9/64

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