We plan to put Beauty to sleep by chemical means, and then we'll flip a (fair) coin. If the coin lands Heads, we will awaken Beauty on Monday afternoon and interview her. If it lands Tails, we will awaken her Monday afternoon, interview her, put her back to sleep, and then awaken her again on Tuesday afternoon and interview her again.
The (each?) interview is to consist of the one question: what is your credence now for the proposition that our coin landed Heads?
When awakened (and during the interview) Beauty will not be able to tell which day it is, nor will she remember whether she has been awakened before.
She knows the above details of our experiment.
What credence should she state in answer to our question?
Is the answer 1/2 or 1/3?
2007-06-22 07:48:44 · 4 answers · asked by The Question 1 in Science & Mathematics ➔ Mathematics
Please justify why it is NOT 1/3 or 1/2. I find *both* answers compelling, so just saying why it is 1/2 or 1/3 is insufficient.
2007-06-22 08:10:19 · update #1
If I interpret this bizarre setup correctly, then when she finds herself being interviewed, there are three possibilities:
1) it's Monday and it landed heads
2) it's Monday and it landed tails
3) it's Tuesday and it landed tails
It's a fair coin, so the probability of #1 and #2 are equal; #3 occurs if and only if #2 occurs, so the probability of #2 and #3 are equal.
Since all three are equally probable and only one has the coins landing heads, the answer is 1/3.
This is an odd restatement of other well-known questions that restrict the problem space to 3/4 of the possible outcomes, such as:
You two children are in a house and at least one is a boy. You knock on the door and a boy answers. What is the probability that the other child is a boy?
(Answer: 1/3)
2007-06-22 08:03:44 · answer #1 · answered by Anonymous · 2⤊ 0⤋
I agree with the answer 1/3 and its explanation. Beauty knows that she will be awakened more times on tails than on heads, so the mere fact that she is awake raises the probability of tails and decreases the probability of heads.
2007-06-22 11:06:18 · answer #2 · answered by TFV 5 · 0⤊ 0⤋
it is merely the result from loss of sleep. All you could fairly do is sleep as much as possible, in step with danger get extra beneficial than 8 hours of sleep, and exercising usually, that may teach you how to get extra drained and ensures you will visit sleep early.
2016-09-28 07:37:04 · answer #3 · answered by ? 4 · 0⤊ 0⤋
Hi. 1/2. There is only one coin toss.
2007-06-22 07:52:44 · answer #4 · answered by Cirric 7 · 0⤊ 0⤋