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Prabha Seshadri
Asked: 2022-11-08T17:43:02+05:30 In:

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let `3/4`be the probability that he knows the answer and `1/4`be the probability that he guesses. Assuming that a student who guesses at the answer with probability 1/4. what is the probability that the student knows the answer given that he answers correctly.?

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let `3/4`be the probability that he knows the answer and `1/4`be the probability that he guesses. Assuming that a student who guesses at the answer with probability 1/4. what is the probability that the student knows the answer given that he answers correctly.?
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  1. Probablity student knows the answer, `P(A) = 3/4`
    Probablity student knows the answer, `P(B) = 1/4`
    Probablity of correct answer when student knows the answer,`P(C/A)= 1`
    Probablity of correct answer when student guesses the answer,`P(C/B)= 1/4`
    So, probablity student gives answer correctly, when he knows the answer,
    `P(A/C) = (P(A)*P(C/A))/(P(A)*P(C/A))+(P(B)*P(C/B))`
    `=(3/4*1)/((3/4)+(1/4)(1/4))=(3/4)/(13/16)=12/13`

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Himanshu Vora
Asked: 2022-11-04T16:32:06+05:30 In:

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 . What is the probability that the student knows the answer given that he answered it correctly?

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 . What is the probability that the student knows the answer given that he answered it correctly?

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  1. Let E1 : the event that the student knows the answer and E2 : the event that the student guesses the answer. 

    Then, E1 and E2 are mutually exclusive and exhaustive. Moreover, 

    P(E1) = 3/4 and P(E2) = 1/4 

    Let E : the answer is correct. The probability that the student answered correctly, given that he knows the answer, is 1 i.e., P P(E/E1) = 1 

    Probability that the students answered correctly, given that the he guessed, is 1/4 

    i.e., P(E/E2) = 1/4

    By using Baye’s theorem, we obtain

    P(E1/E) = (P(E1)P(E/E1))/(P(E1)P(E/E1) + P(E2)P(E/E2))

    = (3/4 x 1)/(3/4 x 1 + 1/4 x 1/4) = (3/4)/(3/4 + 1/16) = (12/16)/(12 + 1)/16 = 12/13

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