@Victor Eremita,
The thought process presumably goes something like this:
1. The two options appear equally valid.
2. I must choose one of them; failure to choose would be irrational.
3. Since I have no other means of deciding, I will choose whichever option happens (by chance) to come more prominently into my mind after this moment.
4. Option B has come more prominently into my mind.
5. Therefore, I choose option B.
Steps 3-5 of course happen very rapidly, so we are barely aware of them as separate steps.
One could use various terms to explain step (4), e.g. chance, randomness, quantum uncertainty. But there doesn't seem to be anything particularly 'absurd' about it. I don't think it's a profound philosophical question.