[chongli]

You can’t do that though. There are only 5 marbles of each colour so there’s no way to split them so that both bags have the same distribution. Thus your closest to 50/50 would be 2 black and 2 white in one bag, 3 black and 3 white in the other, giving you a 0.5 probability of guessing correctly.

You’re better off putting one black marble into one bag and all of the rest of the marbles into the other. That way if you pick the bag with just one marble you win by default and if you pick the other bag you have a 4/9 probability of getting a black one. This gives you a total probability of 13/18 = 0.72.