The Sleep Experiment

To make a quick buck, you volunteer for a strange experiment. The details of the experiment are explained to you before you start.

You arrive on a Sunday and are put to sleep. A fair coin is tossed to decide what happens next.

• If the coin comes up heads, you're awakened on Monday only and the experiment ends there.
• If the coin comes up tails, you're awakened on Monday, put back to sleep with a pill, and awakened again on Tuesday. That pill also erases the memory of your last awakening.

This means that whenever you are woken, you do not know what day it is. And each time, the researchers ask you the same question:
“What do you now say is the probability that the coin landed heads?”

So if you are partaking in the experiment and being awakened with that question... what is your answer?