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Grade 12th PassEngineering Entrance Exams

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is corret.The probability that a student know the answer to a question is 9/10.If he gets the correct answer to a question, then the probability that he was guessing is

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Profile image of Vijay kumar patibanda
13 Years agoGrade 12th Pass
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1 Answer

Profile image of pratiksha agarwal
13 Years ago

E1=he guesses the answer

 E2=he knows the answer

 given P(E2)=9/10

 as they are mutually exclusive then P(E1)+P(E2)=1

 so P(E1)=1/10

 A=he answers correctly

 P(A/E1)=he guesses and answers correctly=1/4

 as there are 4 options and only one can be correct by guessing

 P(A/E2)=he gives correct answer as he knows the answer=1

  if one knows the answer he will obviously give correct answer

 now using baye''s theorem

 P(E1/A)=we know answer is correct and we have to take out probability that he guessed and gave correct answer=

 P(E1)*P(A/E1)/(P(E1)*P(A/E1)+P(E2)*P(A/E2))

 putting values one can find answer.


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