Question Number 131847 by pticantor last updated on 09/Feb/21
![Let (𝛀,ϝ,P) be a probalistics space show that, A,B∈ϝ if (P(A∣B)≤P(A) and P(B∣A)≪P(B)) then P(A∣B^_ )≥P(A)](https://www.tinkutara.com/question/Q131847.png)
$$\:\boldsymbol{{Let}}\:\left(\boldsymbol{\Omega},\digamma,\boldsymbol{{P}}\right)\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{probalistics}}\:\boldsymbol{{space}}\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}},\: \\ $$$$\boldsymbol{{A}},\boldsymbol{{B}}\in\digamma \\ $$$$\boldsymbol{{if}}\:\left(\boldsymbol{{P}}\left(\boldsymbol{{A}}\mid\boldsymbol{{B}}\right)\leqslant{P}\left(\boldsymbol{{A}}\right)\:\boldsymbol{{and}}\:\boldsymbol{{P}}\left(\boldsymbol{{B}}\mid\boldsymbol{{A}}\right)\ll\boldsymbol{{P}}\left({B}\right)\right) \\ $$$${t}\boldsymbol{{h}}{en}\:\boldsymbol{{P}}\left({A}\mid\overset{\_} {\boldsymbol{{B}}}\right)\geqslant\boldsymbol{{P}}\left(\boldsymbol{{A}}\right) \\ $$$$ \\ $$
Answered by guyyy last updated on 13/Feb/21
![](https://www.tinkutara.com/question/18720.png)