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Thread: Finding Probability of Bayesian Network

  1. #1
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    Finding Probability of Bayesian Network

    Finding Probability of Bayesian Network-bayes_nw_hy.png
    I know I can do:
    P(~s|~y, ~h) = P(~s|~y)*P(~h|~y)

    problem is P(~s|~y) and P(~h|~y) are not given and i'm not sure how to find their probabilities.
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  2. #2
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    Re: Finding Probability of Bayesian Network

    We have to assume the decisions of Yale and Harvard are independent of one another.

    Let's first look at the event $Y^c \wedge H^c$

    $P[Y^c \wedge H^c] = P[Y^c \wedge H^c |S]P[S] + P[Y^c \wedge H^c |S^c]P[S^c]$

    $P[Y^c \wedge H^c |S] = P[Y^c|S]P[H^c|S] = (1-P[Y|S])(1-P[H|S]) = (1-0.94)(1-0.87)=0.0078$

    Similarly

    $P[Y^c \wedge H^c | S^c] = (1-0.15)(1-0.12) = 0.748$

    $P[Y^c \wedge H^c] = (0.0078)(0.005) + (0.748)(0.995) = 0.744299$

    Now

    $P[S^c | Y^c \wedge H^c] = \dfrac{P[ Y^c \wedge H^c | S^c]P[S^c]}{P[Y^c \wedge H^c]}$

    $P[S^c | Y^c \wedge H^c] = \dfrac{(0.748)(0.995)}{0.744299} = 0.999948$
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