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Topic: Reverse probabilities - why?

I welcome! Torments a question: why in bayesian probability probability of joint approach often events express through 1 minus product of reverse probabilities? What sense in it? For example, P (y=1|x1, x2) = 1 - (1 - p1) * (1 - p2) where P (y=1|x1, x2) - probability of approach of event y=1, depending on presence of factors x1 and x2, pi - probability of appearance of the factor xi

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Re: Reverse probabilities - why?

Hello, paul.marx, you wrote: PM> I Welcome! PM> torments a question: why in bayesian probability probability of joint approach often events express through 1 minus product of reverse probabilities? What sense in it? PM> for example, PM> P (y=1|x1, x2) = 1 - (1 - p1) * (1 - p2) PM> where PM> P (y=1|x1, x2) - probability of approach of event y=1, depending on presence of factors x1 and x2, PM> pi - the probability of appearance of the factor xi Can simply intuitively easier and more clear by contradiction

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Re: Reverse probabilities - why?

Hello, Sharov, you wrote: S> Hello, paul.marx, you wrote: PM>> I Welcome! PM>> torments a question: why in bayesian probability probability of joint approach often events express through 1 minus product of reverse probabilities? What sense in it? PM>> for example, PM>> P (y=1|x1, x2) = 1 - (1 - p1) * (1 - p2) PM>> where PM>> P (y=1|x1, x2) - probability of approach of event y=1, depending on presence of factors x1 and x2, PM>> pi - the probability of appearance of the factor xi S> Can simply intuitively easier and more clear by contradiction yes is not present, there any deep thought behind this all is covered. Only it disappears from me. But here already on a statement in a type from reverse, removing the brackets we receive P (y=1|x1, x2) = p1 + p2 + p1*p2 instead of as in forehead P (y=1|x1, x2) = p1*p2 so behind all it something should be...

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Re: Reverse probabilities - why?

Hello, paul.marx, you wrote: PM> P (y=1|x1, x2) = 1 - (1 - p1) * (1 - p2) it is simple reviewing from a position of "probability of an error" is admissible, we see in the code a word helper. Probability that it  - 90 %. Nearby still we see that indents in two gaps - we know that it  in 70 % of cases. How to combine both facts? At assumptions  these  the facts, probability that it , at  the facts x1 and x2 = 1 - (1 - 90 %) * (1 - 70 %) = 1 - 0.03 = 97 %. That is "this-govnokod" statement will be incorrect in 3 % cases

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Re: Reverse probabilities - why?

Hello, paul.marx, you wrote: PM> I Welcome! PM> torments a question: why in bayesian probability probability of joint approach often events express through 1 minus product of reverse probabilities? What sense in it? PM> for example, PM> P (y=1|x1, x2) = 1 - (1 - p1) * (1 - p2) PM> where PM> P (y=1|x1, x2) - probability of approach of event y=1, depending on presence of factors x1 and x2, PM> pi - probability of appearance of the factor xi the Formula is true for a case if y it is cocked in 1 at approach x1 OR x2. The analysis of possible outcomes shows that y becomes 1 if happens x1 EITHER happens x2 OR happen (x1 And x2). Y remains 0 if do not happen NEITHER x1 NOR x2. Also it is clear (y it is equal 0 or 1) P (y=1) + P (y = 0) = 1 From here Probability of that do not happen NEITHER x1 NOR x2 for independent events it is equal (1 - p1) * (1 - p2). For P (y=1) it is received: P (y=1) = 1 P (y = 0) = 1 - (1 - p1) * (1 - p2)

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Re: Reverse probabilities - why?

Hello, paul.marx, you wrote: PM> I Welcome! PM> torments a question: why in bayesian probability probability of joint approach often events express through 1 minus product of reverse probabilities? What sense in it? Such that events p1 and p2 can come simultaneously. And if we simply add 1 and 2 probability of that happens both, we consider twice, that is it should be subtracted. Enters 1 + 2 - 1 * 2 = 1 (1 - 2) + 2 = 1 (1 - 2) + 1 - (1 - 2) = 1 - (1-r1) (1-r2)... But, if to note that us the probability of interests that (1-r1) and (1-r2) do not come simultaneously 1 - (1-r1) (1-r2) it is possible to write down at once...