Thanks, that is very clear. You are distinguishing the probability of heads given awakening event as a separate thing from the probability of the tossed coin being heads. Looks to me like the word credence (mental acceptance as true or real) has two different domains depending on whether inside...
Ibex
Once started, the only event known to have occurred is the coin toss and the Monday waking.
She may awake either two or three times, that last time on Wednesday in which she will not know if it is Monday, Tuesday, or Wednesday until they announce the end of the project.
When she awakes at...
its the probability of awakenings before Wednesday
... from Ibix's link...
"I’ve just observed an event (D = waking up before Wednesday) that is twice as likely under the tails scenario..."
I'm not seeing the twice as likely; the Monday waking is certain (p=1), the Tuesday waking based on coin...
I going to go look at theory of conditional probabilities ... (Wikipedia)
P(A|B)=(P(A^B))/P(B)
Where "^" is intersection
and
B is Monday awakening
A is Tuesday awakening
P(B)=1
P(A)=.5
P(A|B)= P(.5^1)/1=.5
Can you reconcile the two different questions having different answers?
Actions that depend on the coin do not include Monday. What happens Monday is strictly determined up to asking SB's credence; why would Monday be included?
How do actions that depend on the known outcome of the coin...
The Monday awakening is unconditional, independent of the coin flip result, independent of when the coin is flipped, and independent of when the result is observed. The experiment does not really begin until Tuesday, the Tuesday awakening conditional on the coin flip, independent of Monday. What...
I think .5 is the answer.
The order of events:
Complete information about the experimental procedure is explained to SB
A fair coin is flipped, SB does not know the result
Sunday evening:
- some analyses explore SB's hypothetical credence of Heads assessed Sunday evening (and maybe Wednesday...
You're right... I see 20 coherent solutions that follow the replies and sum to 11.
Only if Kurt ate 5 will present a unique solution...
A B G K
========
1 2 3 5 <------- unique solution for Kurt
1 2 4 4
1 3 3 4
1 3 4 3
1 4 3 3
1 4 4...
Thinking about the "Aha" question has made me believe Kurt is the first to know unless George ate 2 apples, then George is the first to know!
Alonso's question reveals he either ate 1, 2, 3, or 4 apples
Bert's reply reveals he either ate 1, 2, or 3 apples
George's reply reveals he either ate 1...
Hi Dale, what are your thoughts on this?
It is based on the stipulation
"...by only asking questions that they didn't know the answers to."
Alonso asks "Bert, did you eat more apples than I did?"
Alonso can only ask this question not knowing the answer only if he did not eat more than 4...
I was doing some probability calculations that include squaring a number between 0 and 1.
When I approximate 2/3 using 0.6 or 0.66 or 0.666 etc. I get an interesting series of growing same digit segments...
0.6^2=0.36
0.66^2=0.4356
0.666^2=0.443556
0.6666^2=0.44435556
0.66666^2=0.4444355556...
Hope it's OK to add a question here. I think to pertains to the topic.
What did cosmologists mean by "looks the same from everywhere"? Were they adjusting and calculating to compare "distant local" to "nearby local"? Or were they comparing raw values?
There was a time when both expansion...
OK, thanks; I was using "yes" meaning for all numbers of the set with no exceptions or conditions attached.
Is there an "exclusive yes" like exclusive or?
Here is what I think I know... :)
binary operation - defined on any set if it takes two elements from the set and returns a single element from the same set
additive identity - elements in a set remain unchanged with addition of the additive identity
multiplicative identity - elements in a set...