Need help with NCR type question??

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

home.

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 DON’T have a bag that has a RED ball in it?

I suspect the way to work it out is... (1.0 – The probability I do

have a bag with a RED ball in it).

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I need the most simplified formula for this.