After last week's oldie but goldie, which might not last much longer, this week we pose a much harder problem, that was first considered in the 1980s, and is still puzzling people.
The problem concerns a sleep experiment, which takes the following form.
The subject takes a sleeping draught on a Sunday and after the subject is asleep a fair coin is tossed.
- If the coin falls as a head the subject is woken on Monday and questioned, and the experiment ends.
- If the coin falls as a tail the subject is woken on Monday and questioned, given more of the sleeping potion, is woken on Tuesday and questioned, and the experiment ends.
The drug that the subject takes also has an amnesiac effect, and so they can't remember if they have been woken before or not.
Each time the subject is woken they are asked "What do you believe the probability of the coin falling as a head to be?"
And the problem that you have to resolve is - what is the correct answer to that question?
Answer at 9.00 on Monday