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Re: A question on conditional probability!
Posted:
May 26, 2006 3:56 PM
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Duncan Smith wrote:
> Sticker wrote:
> > I have a question, how to calculate the probability as following:
> > P(A1 & A2 & A3 | B)?
> > Given the condition that event B happens, how to calculate the
> > probability of all A1, A2 and A3 happen? Here A1, A2, A3 are
> > independent with each other but they are dependent with B separately.
> >
> > Can I say:
> >
> > P(A1 & A2 & A3 | B) = P(A1 | B) * P(A2 | B) * P(A3 | B)?
> >
>
> That's OK if the As are conditionally independent given B, but you seem
> to be saying they are not.
>
> Duncan
As Duncan said it is not clear that what is the relationship among As +
B., let ma give an example about conditional independence.
Suppose John and Jan each toss a coin I give(EVENT B) separately. Let
A1 represent John's toss outcome, and A2 represent Jan's toss outcome.
It would be reasonalbe assuming that A1 and A2 are independent for a
coin I give(EVENT B). However A1 is related to B and so is A2 in a
sence if a coin I give is biased toward head/tail.
In this example your formula is correct.
HTH
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