So we're all feeling a bit sick now.
Camy is writing a short story for St Valentine's day. So I thought I'd try to do the same thing. 13 days to write a few thousand words - shouldn't be too difficult. Especially as I keep having ideas for stories.
While researching an aspect of the story on Google, I bumped into something I'd forgotten about: The Sleeping Beauty Probability Problem.
Sleeping Beauty agrees to take part in a scientific experiment. The scientists explain to her that this is what will happen:
She will go to sleep on Sunday, and on Monday they will flip a fair coin. If it comes up heads, they'll wake her up and the experiment will end. If it comes up tails, they'll wake her up, and then give her a sleeping potion that will also make her forget that she had been woken up a few minutes before, and wake her up again on Tuesday.
During the experiment, Sleeping Beauty is woken by the scientists, and asked what the probability is that the coin came up heads. What should she answer?
There are two different answers - 1/2 and 1/3 - to slightly different interpretations of the question.
In the first interpretation, Sleeping Beauty knows only that the coin has been flipped once, and there's a 50% chance of it coming up heads and 50% tails. All the stuff about potions and forgetting doesn't change that, so the answer is 1/2.
In the second interpretation, there are three possibilities. Either:
(1) The coin came up heads, this is the first time she's been woken, it's Monday, and the experiment is about to end.
(2) The coin came up tails, this is the first time she's been woken, it's Monday, and the scientists are about to give her the sleeping potion.
(3) The coin came up tails, she's been woken before but doesn't remember it because of the potion, so this is the second time she's been woken and it's Tuesday.
That is:
(1) Heads, Monday
(2) Tails, Monday
(3) Tails, Tuesday
(There's no "Heads, Tuesday" because if the coin came up heads she'll be woken on Monday and not sent back to sleep. If it came up heads, the probability of the day being Tuesday is zero.)
Sleeping Beauty has no way of knowing whether the coin came up heads or tales, and she has no way of knowing whether it's Monday or Tuesday. But she does know there are three equally likely possibilities, only one of which involves the coin coming up heads. So the answer is 1/3.
There is another question lurking behind that one: If you haven't been educated about probability, how likely are you to be able to work out the answer for yourself?
It's possible, but not likely. And that's why logic puzzles and IQ tests show what kind of education you've had, not how intelligent you are. Whatever that means anyway.
And that's why Mensa is a load of crap.
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