Pinball and Probability

When I was in middle school, I used to play a lot of pinball-- I was pretty good at it, but not so good at math. Anyway, after I had racked up a couple of credits, I'd play several games at once, because I thought I was increasing my chance of getting a free game by way of a match.

It's occurred to me today (I just bought my own pinball machine) that my math was way off-- if I used eight games to match two numbers, instead or eight different numbers, I increased the chance of one of the target numbers getting a match, (2/5, instead of 1/10) but that had nothing to do with winning a free game. Played one at a time, or four at a time, each game had just a 1/10 chance of matching-- assuming that the match numbers really are random. I don't know enough about pinball to say that they are.

So: eight numbers with a 1/10 chance each is the same as two numbers with a 2/5 chance each, right? (It's been ten years since the one math class college required of me.) 2 x 2/5 = 4/5, and 8 x 1/10 = 4/5 also. Did I set that up right? Can someone who's better at math confirm my current thinking?

Also, anyone out there know for sure if the match numbers in pinball are really random?


------------------
------------
--Rowan
Shopping is still cheaper than therapy. --my Aunt Franny