r/probabilitytheory • u/NeighborhoodAny8028 • 9d ago

[Education] Bayes theorem feeling complex

Is bayes theorem really difficult or am I dumb? I couldn't seem to grasp the concept of it. Are there any prerequisites to understanding the theorem ? I only know the basics of probability for now and I am studying it. Please let me know.

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u/lysker 9d ago

It can be very difficult, but it doesn't need to be.

Take two events, "A" and "B." The probability of A and B, if they're independent, is just the product, P(A)*P(B). If they're dependent, then we can just condition one on the other. P(A) * P(B|A), the probability of A times the probability of B given that A is true. This is symmetric, we can do the same thing with P(B) * P(A|B). Both give us the probability of A and B, we just start with A or we start with B.

And we're done. That's the theorem. P(A) * P(B|A) = P(B) * P(A|B). Divide both sides by P(A) or P(B) to get it in the form you're probably expected to memorize.

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u/mfb- 8d ago

to get it in the form you're probably expected to memorize.

I really dislike that courses will usually use that form. Written as P(A and B) = P(A) * P(B|A) = P(B) * P(A|B) it is completely intuitive.

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u/lysker 8d ago

Wholeheartedly agree.