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Math Help - Word problem

  1. #1
    Member javax's Avatar
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    Word problem

    I need some help and clarifications on such problems. For example:

    A student thinks he will succeed on subjects "Probability", "Statistics" and in both of them with the probabilities 0.7, 0.6 and 0.5 respectively. Find the probabilities:
    1). p1: The student will succeed at least in one of the subjects
    2), p2: The student will succeed only in one of the subjects
    3), p3: The student will succeed not more than in one subject
    result: p1 = p2+p3

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  2. #2
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    Quote Originally Posted by javax View Post
    I need some help and clarifications on such problems. For example:

    A student thinks he will succeed on subjects "Probability", "Statistics" and in both of them with the probabilities 0.7, 0.6 and 0.5 respectively. Find the probabilities:
    1). p1: The student will succeed at least in one of the subjects
    2), p2: The student will succeed only in one of the subjects
    3), p3: The student will succeed not more than in one subject
    p_1=P(P)+P(S)-P(B)
    p_2=P(P)+P(S)-2P(B)
    p_3=1-P(B)
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  3. #3
    Member javax's Avatar
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    Quote Originally Posted by Plato View Post
    p_1=P(P)+P(S)-P(B)
    p_2=P(P)+P(S)-2P(B)
    p_3=1-P(B)
    ok thanks, would you please explain how you derived formulas for p2 and p3?
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  4. #4
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    Quote Originally Posted by javax View Post
    ok thanks, would you please explain how you derived formulas for p2 and p3?
    Exactly one:
    p_2=P\left( {A \cap B^c } \right) + P\left( {A^c  \cap B} \right) =  \left[ {P(A) - P\left( {A \cap B} \right)} \right] + \left[ {P(B) - P\left( {A \cap B} \right)} \right] = \left[ {P(A) + P(B) - 2P\left( {A \cap B} \right)} \right]

    p_3 is "No more than one" is "not both".
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