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I know and understand that:
P(B|A) = P(AandB)/P(A)
but does...
P(A|B) always = (PAandB)/P(B) as well?
Thanks!
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AND...is this ALWAYS true regardless of whether the events are dependent or independent?
P(AandB) = P(A|B) * P(B) = P(B|A) * P(A)
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Wait, I think I get it.
If the events are independent, then P(AandB) = P(A) * P(B)
If the events are dependent, then P(AandB) = P(A/B) * P(B)
Is that right? I sure hope so.
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Quote:P(B|A) = P(AandB)/P(A)
P(A|B) always = P(AandB)/P(B)
This is correct. The numerator is always P(AandB) for Bayes Theorem. The denominator is the probability which the outcome depends on (tip: it's always the alphabet on the right hand).
P(A|B) can be defined as the probability of A happening on the condition that B happens.
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In regards to your first post, keep in mind that A and B are just random variables. They could represent any number and thus are interchangable
Edit: I just realized that this post was from over a month ago. Whoops! thought it was only a few days old
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