"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."
"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."
"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."
"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."
"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."
"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."