[pendragon]

All these answers under 50% have to be wrong, right? That can't be right, the 10 red ball bag has to be more likely than the 5/5 bag.

This is a Bayes Theorem issue, so:

Event A = the bag is the 10 red ball bag
Event B = 2 red balls picked

P(B|A) = 1 (only red balls in this bag)
P(A) = .5 (either bag equally likely)
P(B) = 15/20*14/19 = .55263 (I'm not entirely sure about this one...it might also be .5*(1^2+.5^2)=.625)

So P(A|B)=1*.5/.55263=90.476%
Or 1*.5/.625=80% (I think this is it actually)

If I'm wrong it's probably about P(B), but I'd say the answer has to be above 50%.

Edit: Nevermind, I didn't realize that the bag was spun twice [img]/images/graemlins/smile.gif[/img] Bruce already did it.