#Derivation of conditional probability formula

33 messages · Page 1 of 1 (latest)

stiff oriole
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Helloo, it's been sometime that I didn't touch probability and conditional probability. When it comes to conditional probability I know we read it like that most of the time: Given event A, what is the probability that event B occurs? P(B | A).

For us to calculate something like that, normally I would just look how the formula look like but I wanted to know how it's derive, so I can use it "naturally" without trying to remember the formula. Would really appreciate if someone can explain its derivation or a nice way of how to remember it

drifting hornetBOT
gusty wave
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its the chance A occurs given that A has occured, reducing your sample space to A
then you find probability of B in A or B intersection A

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can be shown by TPT

stiff oriole
stiff oriole
gusty wave
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Let our sample space consist of A, B and notA intersection notB , P(B | A). means the chance B occurs given that A has occured.
this states that event A has occured, so we do not consider the sample space consiting on not A, and focus on A
P(A) is probability A has occured
now if i can visually show you using a Venn

stiff oriole
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now if i can visually show you using a Venn
would be nice :c

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Am lost with the words 😭

gusty wave
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lets say this is the original sample space

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this has occured

image.png
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and we need to find the red ( Bintersection A)

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now if you know the basic definition of probability = favourable outcomes/total

stiff oriole
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yep

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ah I see

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so it would be P(B n A) / p (A)

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B n A because of the red section

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p (A) because we only want sample space of A?

gusty wave
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so if we were to solely find P( Bintersection A) it would be ( Bintersection A) / 1

gusty wave
stiff oriole
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yepp I see, thanks a lot, now I don't need a formula to memorise that, the venn diagrams were really useful

gusty wave
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you know P(S) = 1

stiff oriole
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yeahh I see

gusty wave
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right

stiff oriole
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yup, that just clicks in my head

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Thanks a lot !!

gusty wave
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that would be theoretical but idk how to derive it tbf using TPT involves application of formula

stiff oriole
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I have a mental model now, I will stick with that :p

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thanks once more

gusty wave
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👍