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In an entrance test there are multiple choice questions there are four possible answer to each question of which one is correct.the probablity that a student knows the answer to question is 90%.if he gets the correct answer to a question then the probablity that he was guessing is?
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In an entrance test there are multiple choice questions there are four...
Probability of Guessing in an Entrance Test
Problem Statement
In an entrance test, there are multiple-choice questions with four possible answers, of which only one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then what is the probability that he was guessing?
Solution
Let's assume that the probability of knowing the answer to a question is P(K) and the probability of guessing the answer is P(G).
Given that the student knows the answer, the probability of answering the question correctly is P(C|K) = 1, and the probability of answering the question incorrectly is P(I|K) = 0, since the student knows the answer.
If the student is guessing the answer, then the probability of answering the question correctly is P(C|G) = 1/4, and the probability of answering the question incorrectly is P(I|G) = 3/4, since there are four possible answers, of which only one is correct.
Using Bayes' theorem, we can find the probability of the student guessing the answer given that he answered the question correctly.
The probability of the student answering the question correctly is given by the formula:
P(C) = P(K) * P(C|K) + P(G) * P(C|G)
Substituting the values, we get:
P(C) = 0.9 * 1 + (1 - 0.9) * 1/4
P(C) = 0.925
The probability of guessing the answer given that the student answered the question correctly is given by the formula:
P(G|C) = P(G) * P(C|G) / P(C)
Substituting the values, we get:
P(G|C) = (1 - 0.9) * 1/4 / 0.925
P(G|C) = 0.027
Conclusion
Therefore, the probability that the student was guessing the answer given that he answered the question correctly is 0.027, or approximately 2.7%.
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In an entrance test there are multiple choice questions there are four...
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In an entrance test there are multiple choice questions there are four possible answer to each question of which one is correct.the probablity that a student knows the answer to question is 90%.if he gets the correct answer to a question then the probablity that he was guessing is?
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