Re: Conditional probabilities beginner questions


<c.dexter.ward@xxxxxxxxxxxxxx> wrote in message
news:1174260269.500998.313290@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi,
I have several beginner questions regarding conditional probabilities
and bayes rule.

1) How to write "Probability of a given (b and c)"?
P(a | b, c) ?

b,c is too confusing because you can't tell whether it's "b and c" or "b or
c".

P (a | bc) or P(a | b and c)

How does the bayes rule work on it?
P(a | b, c) = P(b,c|a)P(a)/P(b,c) ?

P(a | b and c) = P (a and b and c) | P(b and c)

Basically b and c is seen as a single event d=(b and c) and we can
apply directly bayes rule on P(a,d)?

2) How to write "Probability of (a given b) and c"?
P(c,a|b) ?
This depends on how c is affected by b.

Is P(c,a|b)=P(c)P(a|b)P(c|a,b) valid?
You have c showing up twice before "|", that shouldn't make any sense.


3) How to write "Probability of (a and c) given b"?
P(a,c|b)? Something wrong, it is exactly 2).

P(a and c | b). Use "and" or "or" to better clarify your intention.

Assuming this is correct, how does bayes rule work?
Is it just applying the rule on P(d|b) with d=(a and c)?

P(a|b) = P(and b) / P(b). You are saying tha you already know event b
happened so P(b) is your entire universe and treated as 100%. You are now
trying to determine the probability of event a happened under that context.

Thanks for your help.



.

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