If the probability that any one of your beliefs is true is .5, the probability that your cognitive faculties are reliable (.75 or more of your beliefs are true) is 10^-58. Show your work.
My belief is that this is a load of shit.
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Donāt really get the point of this (and havenāt thought about it much), but the ā27ā bit is a citation. It should be 10^-58.
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Thanks
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Whatās so funny?
Nothing. Nothing.
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Weāll, 10^-5827 is almost nothingā¦
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Without doing the math, that sounds about right. If the probability that even just one out of a 1000 beliefs is true is only .5% then it is certainly very unlikely that at least 750 out of 1000 beliefs are true.
My guess here is @OysterOmelet is presenting a problem that gets solved through binomial distribution, or binomial cumulative distribution function.
The text he provided shows 1000 independent beliefs so that would be the total number of events taking place. 0.5 is the probability any one of those beliefs is correct and we would want to know the probability that out of 1000 beliefs 750 of them are correct.
Donāt have time for this myself today though. But that very small number 10^-5827 seems about right as we have strayed very far from the expected mean.
The same problem could be presented as toss a coin 1000 times and ask what are the odds it lands on heads 750 times.
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Itās 50-50 each belief is true.
Oh I got you. Then if you take a sample of 1000 beliefs. You know 50% of all of your beliefs are true (like 20,000). Then you find that 750 out of your sample of 1000 are true, that will also quite unlikely. Is that what they are saying?
Thatād be 750 or more.
But itās 100 beliefs. I donāt know how you guys get 1000.
just toss a coin 1000 times.
Itās in the book you posted.
āIf I have one thousand independent beliefs, for example, the probability (under these conditions) that three quarters or more of these beliefs are true will be less than 10^5827ā
It then goes on to talk about 100 beliefs but that is another number and not the one you posted.
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I was doing this but lost my coin under some furniture.
Do you have a coin?
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I freaking canāt read.
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do thought experiment. roll a sheep 1000 times.
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Looking at the text again it seems like it is 10^58 and the 27 is a footnote.
An online calculator gives roughly the same answer.
perl binomcalc.pl m=cu a=s n=1000 k=750 p=0.5
Probability of success on a single trial (p): 0.5
Number of trials (n): 1000
Number of successes (k): 750
Probabilities:
P( X = k ): <0.0000000000000001 = 4.500981475549265eā59
P( X < k ): >0.999999999999999
P( X ā¤ k ): >0.999999999999999
P( X > k ): <0.0000000000000001 = 2.237146777465939eā59
P( X ā„ k ): <0.0000000000000001 = 6.738128253015204eā59
https://sealevel.info/binomcalc.sphp?n=1000&k=750&p=0.5&m=cu&a=s
or the right number if you round up to the most significant number.
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