The Ninth Bridgewater Treatise a Fragment
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In this case the probability of the occurrence of the event is —, and the probability of the concurrence ot 71 witnesses in falsehood is (- ) • Hence the probability that the particular number i was drawn, as deduced from the testimony of n wit- nesses, each of whose probability of falsehood is -, is expressed by, v p^ ill (, _')"L + (i)"(, _i)( 1 )"- ^ p^ in \p^ V m^ ^m — 1/ (C. ) ^IH 1 1 + {m-l) (=^— -_) 200 APPENDIX.
and the probability of the number i not having been drawn, or of their fals...ehood, is m — 1 {p — 1 . M — 1)" + (m — 1) Hence the improbability of the testimony must, according to Hume, be greater than that of the occur- rence of the event ; or, m — 1 1 {p—\. In—\Y-\-m—\ ^ m ' Hence, m . M—\ m . M — 1 — m—\ ^(w — 1)", •^ 2 locr. (m — I) -^log. (/;-!) + log. {m-D If p=ll, and »i= 1000, 000, 000, 000, as above, 2x12^ 24 + ''>r+i2>Tri>^- If it is only required that the probability of the occurrence of the miracle shall be greater than its APPENDIX.
What to read after The Ninth Bridgewater Treatise a Fragment?
You can find similar books in the "Read Also" column, or choose other free books by Babbage Charles to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In this case the probability of the occurrence of the event is —, and the probability of the concurrence ot 71 witnesses in falsehood is (- ) • Hence the probability that the particular number i was drawn, as deduced from the testimony of n wit- nesses, each of whose probability of falsehood is -, is expressed by, v p^ ill (, _')"L + (i)"(, _i)( 1 )"- ^ p^ in \p^ V m^ ^m — 1/ (C. ) ^IH 1 1 + {m-l) (=^— -_) 200 APPENDIX.
and the probability of the number i not having been drawn, or of their fals...ehood, is m — 1 {p — 1 . M — 1)" + (m — 1) Hence the improbability of the testimony must, according to Hume, be greater than that of the occur- rence of the event ; or, m — 1 1 {p—\. In—\Y-\-m—\ ^ m ' Hence, m . M—\ m . M — 1 — m—\ ^(w — 1)", •^ 2 locr. (m — I) -^log. (/;-!) + log. {m-D If p=ll, and »i= 1000, 000, 000, 000, as above, 2x12^ 24 + ''>r+i2>Tri>^- If it is only required that the probability of the occurrence of the miracle shall be greater than its APPENDIX.
What to read after The Ninth Bridgewater Treatise a Fragment?
You can find similar books in the "Read Also" column, or choose other free books by Babbage Charles to read onlineMoreLess
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