What are the chances of a girl that has been on birth control for about half a year would get pregnant from pre-ejaculate fluid the might have gotten on a finger before I fingered her?
Very unlikely. Especially if she's been taking her birth control correctly
What are the chances of a virgin getting pregnant from if you got a little bit of pre-ejaculate on your finger and wiped it clean with a rag and then fingered her?
The pill is not 100% effective (no birth control methods are 100% effective) so it's possible that you could be pregnant. The chances are low though. To further lower your chances of getting pregnant, perhaps consider also using condoms or another form of birth control (that won't clash with the pill, ie. something non-hormonal) such as the cap.
I've seen this question around and I have already answered it once today and I wonder where this comes from. Of course birth control does not make it easier to get pregnant! Birth control prevents ovulation and you can not get pregnant without a egg. in order to get pregnant you have to quit using any type of birth control. And yes, birth control is not 100% effective but not using it is 0% effective…