Question 347050: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. you go into the exam without knowing a thing, and have to resort to pure guessing?
b. you have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. you have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. you go into the exam without knowing a thing, and have to resort to pure guessing?
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Binomial Problem with p = 1/5 and n = 12
P(9<= x <=12) = 1 - binomcdf(12,1/5,8) = 0.0000623..
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b. you have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
Binomial Problem with p = 1/2 and n = 12
P(9<= x <=12) = 1 - binomcdf(12,1/2,8) = 0.0730
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c. you have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing.
Binomial: with p = 1/5 and n = 10
P(7<= x <=10) = 0.0008643....
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Cheers,
Stan H.
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