Multiple-choice questions each have four possible answers (a, b, c, d), one of w
ID: 3222286 • Letter: M
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) = (Type an exact answer.) 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) = (Type exact answers.) c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made? (Type an exact answer.)Explanation / Answer
As we are guessing the answer and there are 4 choices, then the probability to get it correct would be 1/4 = 0.25
Therefore we get: P(C) = 0.25 and P(W) = 1- 0.25 = 0.75
a) P(WWC) = P(W)P(W)P(C) = 0.752*0.25 = 0.140625
Therefore 0.140625 is the required probability here.
b) P(WCW) = P(W)P(C)P(W) = 0.752*0.25 = 0.140625
Therefore 0.140625 is the required probability here.
P(CWW) = P(C)P(W)P(W) = 0.752*0.25 = 0.140625
Therefore 0.140625 is the required probability here.
c) Based on the above results we see that the total probability of getting exactly 1 correct answer would be:
P(WWC) + P(WCW) + P(CWW) = 3*0.140625 = 0.421875
Therefore 0.421875 is the required probability here.
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