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Version: 1
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"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong.  Posteriors are 0, 1/10, 2/10, 3/10, 4/10 summing to 1."

"The chance of seeing 'RIGHT' next time is 1 + 4 + 9 + 16 divided by 40, 30/40."

Version: 2
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"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong.  Posteriors are 0, 1/10, 2/10, 3/10, 4/10.  The chance of seeing 'RIGHT' next time is 1 + 4 + 9 + 16 divided by 40, 30/40."

"Spelling that out for the new candidates:"

"We start with five hypotheses 0/4, 1/4/, 2/4, 3/4, 4/4, each of which has prior probability 1/5."

"After seeing 'RIGHT' one time, we've got likelihoods-times-probabilities of 0/20, 1/20, 2/20, 3/20, 4/20."

"The relative odds of the posterior will be proportional to that, but it has to sum to 1.  There's 1 + 2 + 3 + 4 = 10 total shares, of twentieths but it doesn't matter what exactly, so the posterior probabilities are 0, 1/10, 2/10, 3/10, 4/10, summing to 1."

"Then if you take the likelihoods off each of those, weighted by the new probability, it's 0 * 0, 1/10 * 1/4, 2/10 * 2/4, 3/10 * 3/4, 4/10 * 4/4, and that's how you get 1 + 4 + 9 + 16 divided by 40 equals 3/4."

Version: 3
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Content

"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong."

"We start with five hypotheses 0/4, 1/4/, 2/4, 3/4, 4/4, each of which has prior probability 1/5."

"After seeing 'RIGHT' one time, we've got likelihoods-times-probabilities of 0/20, 1/20, 2/20, 3/20, 4/20."

"The relative odds of the posterior will be proportional to that, but it has to sum to 1.  There's 1 + 2 + 3 + 4 = 10 total shares, of twentieths but it doesn't matter what exactly, so the posterior probabilities are 0, 1/10, 2/10, 3/10, 4/10, summing to 1."

"Then if you take the likelihoods off each of those, weighted by the new probability, you get 1 + 4 + 9 + 16 divided by 40 equals 3/4."

Version: 4
Fields Changed Content
Updated
Content

"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong."

"We start with five hypotheses 0/4, 1/4/, 2/4, 3/4, 4/4, each of which has prior probability 1/5."

"After seeing 'RIGHT' one time, we've got 'priors-times-likelihoods' of 0/20, 1/20, 2/20, 3/20, 4/20."

"The relative odds of the posterior will be proportional to the 'priors-times-likelihoods', but it has to sum to 1.  There's 1 + 2 + 3 + 4 = 10 total shares, of twentieths but it doesn't matter what exactly, so the 'posterior-distribution' is 0, 1/10, 2/10, 3/10, 4/10, summing to 1."

"Then if you take the likelihoods off each of those, weighted by the new posterior-probability, you get 1 + 4 + 9 + 16 divided by 40 equals 3/4."

Version: 5
Fields Changed Content
Updated
Content

"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong."

"We start with five hypotheses 0/4, 1/4/, 2/4, 3/4, 4/4, each of which has prior probability 1/5."

"After seeing 'RIGHT' one time, we've got 'priors-times-likelihoods' of 0/20, 1/20, 2/20, 3/20, 4/20."

"The 'relative-odds' of the posterior will be proportional to the 'priors-times-likelihoods', but it has to sum to 1.  There's 1 + 2 + 3 + 4 = 10 total shares, of twentieths but it doesn't matter what exactly, so the 'posterior-distribution' is 0, 1/10, 2/10, 3/10, 4/10, summing to 1."

"Then if you take the likelihoods off each of those, weighted by the new posterior-probability, you get 1 + 4 + 9 + 16 divided by 40 equals 3/4."

Version: 6
Fields Changed Content
Updated
Content

"Let us, possibly, try this with five positions before going straight to ten."

"0/4, 1/4, 2/4, 3/4, 4/4 likelihood of yielding RIGHT, all positions equally probable before then."

"We see one 'RIGHT'.  The likelihoods are 0/4, 1/4, 2/4, 3/4, 4/4.  The posteriors are - I see the other two things Pilar did wrong."

"We start with five hypotheses 0/4, 1/4/, 2/4, 3/4, 4/4, each of which has prior probability 1/5."

"After seeing 'RIGHT' one time, we've got 'priors-times-likelihoods' of 0/20, 1/20, 2/20, 3/20, 4/20."

"The 'relative-odds' of the posterior will be proportional to the 'priors-times-likelihoods', but they have to sum to 1.  There's 1 + 2 + 3 + 4 = 10 total shares, of twentieths but it doesn't matter what exactly, so the 'posterior-distribution' is 0, 1/10, 2/10, 3/10, 4/10, summing to 1."

"Then if you take the likelihoods off each of those, weighted by the new posterior-probability, you get 1 + 4 + 9 + 16 divided by 40 equals 3/4."