- #1
sri_newbie
- 2
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Hi Everyone,
I am a newbie in probability theory and following is my question:
Consider we have two binary random variables A and B. B is dependent on A. So we have two conditional probability tables P(A) and P(B|A) with the following parameters :
A P(A)
----------
F 0.3
T 0.7
A P(B=T|A)
------------------
F 0.4
T 0.6
Suppose that A=T is observed. So, now the probability of A being True is 1.0 instead of 0.3 and P(A=F) = 0.0 instead of 0.7. Observing A=T the probability of B=T is going to be 0.4, by just looking up the corresponding tuple in B's CPT. Consider a different scenario where we now observe only B=T. My first question is,
1) is P(B=T) going to be 1.0, since we have observed it, comparing to the first scenario of observing A=T? I know that if nothing is observed then P(B=T) is calculated as P(A=T)xP(B=T|A=T)+P(A=F)xP(B=T|A=F), which is the marginal probability of B=T.
My second question which follows from the first one is,
2) if P(B=T) = 1.0 when B=T has been observed, then while calculating the posterior probability of A=T given B=T i.e. P(A=T|B=T) why is it that we don't put P(B=T)=1.0 in the denominator of the following Baye's rule
P(A=T|B=T) = P(A=T) x P(B=T|A=T) / P(B=T)
Why do we use the marginal value of P(B=T) [when nothing is observed] computed by the expression
P(A=T) x P(B=T|A=T) + P(A=F) x P(B=T|A=F)?
Thanks in advance.
newbie
I am a newbie in probability theory and following is my question:
Consider we have two binary random variables A and B. B is dependent on A. So we have two conditional probability tables P(A) and P(B|A) with the following parameters :
A P(A)
----------
F 0.3
T 0.7
A P(B=T|A)
------------------
F 0.4
T 0.6
Suppose that A=T is observed. So, now the probability of A being True is 1.0 instead of 0.3 and P(A=F) = 0.0 instead of 0.7. Observing A=T the probability of B=T is going to be 0.4, by just looking up the corresponding tuple in B's CPT. Consider a different scenario where we now observe only B=T. My first question is,
1) is P(B=T) going to be 1.0, since we have observed it, comparing to the first scenario of observing A=T? I know that if nothing is observed then P(B=T) is calculated as P(A=T)xP(B=T|A=T)+P(A=F)xP(B=T|A=F), which is the marginal probability of B=T.
My second question which follows from the first one is,
2) if P(B=T) = 1.0 when B=T has been observed, then while calculating the posterior probability of A=T given B=T i.e. P(A=T|B=T) why is it that we don't put P(B=T)=1.0 in the denominator of the following Baye's rule
P(A=T|B=T) = P(A=T) x P(B=T|A=T) / P(B=T)
Why do we use the marginal value of P(B=T) [when nothing is observed] computed by the expression
P(A=T) x P(B=T|A=T) + P(A=F) x P(B=T|A=F)?
Thanks in advance.
newbie