No need to remember the formula. Instead, understand it and u can derive it.
Looking at the diagram above,
- Omega is the entire probability space. [rectangle]
- Event A is a subset of Omega with probability of happening P(A). [left circle]
- Event B is a subset of Omega with probability of happening P(B). [right circle]
- A intersect B is when A and B both happening. [middle ellipsis]
P(B|A) is
- conditional prob of B given A
- ie knowing that A has happened, it is the chance of B happening
What does it really mean?
- knowing that A has happened -> the prob space has shrunk from Omega [rectangle] to P(A) [red circle]
- the chance of B happening left is A intersect B [middle ellipsis]
- note that we don't look at the rest of P(B) [outside of red circle] anymore, since it's outside of the realm of possibility knowing that A has happened.
Picturing the diagram in your mind, you will figure out that
- Given A has happened, chance of B happening is [middle ellipsis] divided by [red circle]
- ie P(B|A) = P(A intersect B) / P(A)
source:
https://courses.edx.org/courses/course-v1:MITx+6.008.1x+3T2016/courseware/1__Probability_and_Inference/conditioning_on_events/
