probability question

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rsen1324
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#1
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#1
So there are two events A and B
I have seen 3 different formulae to calculate the p(AnB):

P(AnB) = P(A) * P(B)
P(AnB) = P(B) * P(A|B)
P(AnB) = P(A) + P(B) - P(AuB)

What is the difference between these 3, and in which situation would I use each one?
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RDKGames
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(Original post by rsen1324)
So there are two events A and B
I have seen 3 different formulae to calculate the p(AnB):

P(AnB) = P(A) * P(B)
P(AnB) = P(B) * P(A|B)
P(AnB) = P(A) + P(B) - P(AuB)

What is the difference between these 3, and in which situation would I use each one?
Generally, if you don't know anything about how A,B are related, then

(*) P(AnB) = P(B) * P(A|B)
(**) P(AnB) = P(A) + P(B) - P(AuB)

are both valid and equivalent to use. Just depends on what info you have. On one hand you might have the conditional probability, on the other you might instead know the union probability. So using one over the other depends on this scenario.

(*) is actually what you use when doing tree diagram probabilities, and (**) is more common in venn diagrams.

However, if A,B are independent, then this implies that P(A|B) = P(A) which means (*) becomes

(***) P(AnB) = P(A) * P(B)

which is why you can only use (***) when A,B are independent.
Last edited by RDKGames; 1 month ago
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rsen1324
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#3
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(Original post by RDKGames)
Generally, if you don't know anything about how A,B are related, then

(*) P(AnB) = P(B) * P(A|B)
(**) P(AnB) = P(A) + P(B) - P(AuB)

are both valid and equivalent to use. Just depends on what info you have. On one hand you might have the conditional probability, on the other you might instead know the union probability. So using one over the other depends on this scenario.

(*) is actually what you use when doing tree diagram probabilities, and (**) is more common in venn diagrams.

However, if A,B are independent, then this implies that P(A|B) = P(A) which means (*) becomes

(***) P(AnB) = P(A) * P(B)

which is why you can only use (***) when A,B are independent.
Ah alright, I understand. Thanks a lot!
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