# Thread: Finding Probability of Bayesian Network

1. ## Finding Probability of Bayesian Network

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.

2. ## 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

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

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