You can create a variable that saves a random number and then uses this variable to assist with skipping logic.
Insert this SSI Script in to the footer of a prior question. Ensure this question is not skipped over as we need it to evaluate for every survey.
Now define "RandNum" as a Pass-In field variable and define it as a whole number.
Now use the following in your skip logic ...
Skip To: Q3
Skip Logic: Q1=2 and RandNum=2
So all "Q1=1 and RandNum=1" will continue through to Q2.
I have assumed the following ...
*Your question order is Q1-Q2-Q3 ...
*Q1 is a single response select question.
If you wanted to apply a stricter 50%-50% split for those who answered B at Q1, you could use a least fill quota approach. You would ignore the RandNum variable approach and setup a quota question with 2 options (B1 and B2) and select the least fill option. You skip logic will operate off the quota question.