Is P(x) = P(x | y )*P(y) + P(x | ~y )*P(~y) according to Bayes theorem?

[sallu110]

Can anyone tell me if this equation valid? If yes how? I have tried to check on google but couldn't find it! If this equation is valid then I will be able to solve a question on Bayes theorem. Thanks!

 

[hlsmith]

~y represent complement to y? Do you have a dataset to go along with this or could you create a toy set?

 

[sallu110]

~y represent complement to y? Do you have a dataset to go along with this or could you create a toy set?

Yes! ~y represents a complement to y!

 

[hlsmith]

Well let us see if you can beat me, but tomorrow I will make a toy example and see if the above holds.

 

[Dason]

It does. Definition of conditional probability and law of total probability. Maybe need one other piece but yeah it works

 

[sallu110]

Thanks @Dason @hlsmith

 

[hlsmith]

Dummy me just did it by hand and they were equal.

2x2 matrix: 10, 12, 15, 20.
p(x) = (22/57) = ((10/25) * (25/57)) + ((12/32) * (32/57))
0.386 = 0.386

 

[Dason]

It's easier just to apply all of those probability laws in your head to verify the identity. Just a tip for next time

 

[hlsmith]

epitaph: Applied until the day he died.