First, label the four balls.

Might as well do 1 and 2 black balls.

No.3 and No.4 are white balls.

Then * * * has A44=4*3*2* 1=24 arrangements.

Among them, black and white has 1*2*, and 34 and 43 can be filled in *.

The asterisk can be filled with 2* 1*, 34 and 43.

* 1*2, in the same way, two kinds.

*2* 1, similarly, two kinds.

There are 2 * * * 4 = 8 kinds in total.

8÷24= 1/3, that is, the probability of Party A winning (black and white) is 1/3.

So choose Party B..