I need help with the following for some hobby-programme Iím writing at

There are A bags that contain either a single RED or single BLACK ball.
B of the bags have a single RED ball in them B <= A
I have C of the bags in my possession C <= A

What is the probability that I DONíT have a bag that has a RED ball in it?

I suspect the way to work it out is... (1.0 Ė The probability I do
have a bag with a RED ball in it).


I need the most simplified formula for this.