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Yttrium
 one year ago
Can somebody explain me the sense of using the Baye's Law of probability and the total probability theorem? Thanks.
Yttrium
 one year ago
Can somebody explain me the sense of using the Baye's Law of probability and the total probability theorem? Thanks.

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SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.0Suppose you have a tree of possible events like the one below: dw:1385668006646:dw Then, Baye's law says that the probability of one event on the far right (say \(\alpha\)), given that one of the preliminary events (say \(A\)) has occurred, is given by \[P(\alphaA)=\frac{P(A\alpha)P(\alpha)}{P(A)}=\frac{P(A\alpha)P(\alpha)}{P(A\alpha)+P(A\beta)+P(A\Gamma)}\] Basically, it says that the probability of some event \(A\) occurring, given the occurrence of another event \(\alpha\), is given by the ratio of (1) [the probability of \(A\) and \(\alpha\) occurring together] to (2) [the total probabilities of \(A\) occurring]. (1) The probability of two events occurring together is \(P(A\cap\alpha)\). Using the conditional probability definition, we get \(P(A\alpha)=\dfrac{P(A\cap\alpha)}{P(\alpha)}\), i.e. \(P(A\cap\alpha)=P(A\alpha)P(\alpha)\). (2) The total probability theorem is another way of saying that the denominators in the above equation are the same.
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