Probability Formula Question

[soliloquy]

I know and understand that:

P(B|A) = P(AandB)/P(A)

but does...

P(A|B) always = (PAandB)/P(B) as well?

Thanks!

[soliloquy]

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)

[soliloquy]

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.

[laughter]

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.

[jdsdog10]

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