I'm struggling trying to understand bayesian network.

Having trouble finding P(F&G)

I know independence and conditional independence are different things. Conditional independence is when A node is conditionally independent of its non-descendents, given its parents and Independent events are events where the outcome of one has no effect on the possible outcome of another.

I was wondering for this case if it's possible to use P(F&G)=P(F)*P(G)? I would really highly appreciate if anyone can explain to me why or why not and possibly the start of the calculation. I've been stuck for days.

  • 1
    $\begingroup$ There is no reason to expect $F$ and $G$ to be independent as, for example, they are each affected by $D$ $\endgroup$ – Henry Mar 17 '18 at 19:10
  • $\begingroup$ Yes that's what i thought so too but i have friends trying to convince me it is independent. Is it possible for you to help me start off or guide me in the right direction for calculating this? $\endgroup$ – shannon901 Mar 17 '18 at 20:45
  • $\begingroup$ There are $2^7=128$ conceivable combinations though a large majority have probability $0$. I suggest you work out the probability of each based on $A$ and $B$ being independent and each having probability $0.3$ $\endgroup$ – Henry Mar 17 '18 at 21:56

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