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Math Help - Probability Question: 2 students and 1 professor

  1. #1
    Popo
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    Probability Question: 2 students and 1 professor

    Hi, someone please help me with this problem?

    A professor ask a series of question to 2 students, A and B. If the students dont know the answer then they dont answer. If they think they have an answer then they answer.

    For any question, A doesnt know if B can answer nor the answer of B (if B can answer). The same for B.

    Before the test begins, the probability that an answer of A is good is unknown. The same thing for B.

    Now, the test begins. Here is the score-sheet of the 2 students after many many questions:

    For A: he has answered to 50 questions, with 40 good answers and 10 wrong. (80% good)
    For B: he has answered to 75 questions, with 30 good answers and 45 wrong. ( 40%good)

    By some calculus, the professor find that :
    1/ The probability that the next answer of A is good is 0.8
    2/ The probability that the next answer of B is good is 0.4
    Suppose that (1) and (2) are correct.

    Now, the professor ask the 2 students one more question. This time, both A and B think they can respond, and by CHANCE they give the same answer.

    The question is: what is the probability that this answer, given by both A and B, is a good answer?

    Uhmmmm....

    I think this probability must line between 0.4 and 0.8 ; maybe (0.4+0.8)/2 = 0.6 ???

    Thank you in advance

    Popo
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  2. #2
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    It seems that P(A) and P(B) are independent probabilities that means P(A and B) = P(A)*P(B)
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