text_combined: rich neapolitan bfjgyyrpxggbneiuedu thank responded query discussed matter resolution first ill redescribe problem using numbers terminology provided francisco javier diez suppose task psuccess 0001 someone clairvoyant psuccess 1 someone clairvoyant idea whether population includes clairvoyants least want impose prior beliefs mike claims one null hypothesis succeeds unlikely event occurred 0001 null hypothesis true reject hypothesis believe mike probably one next 10000 people making claims clairvoyants null hypothesis none null hypothesis true probability least one succeeding 1999910000 63 mike alone succeeds reason reject null hypothesis need quite people succeeding reject little reason believing mike anyone else group clairvoyant way insist obtaining beliefs hypothesis testing however ij good said dont sweep prior beliefs carpet solve problem using bayes theorem suppose believe 01 probability individual say mike clairvoyant pclairvoyantsuccess psuccessclairvoyantpclairvoyantpsuccessclairvoyantpclairvoyant psuccessnot clairvoyantpnot clairvoyant 1 x 01 1x 01 0001 x 99 99 mike succeeds believe probably clairvoyant regardless many people attempt task succeed applications situations like buffet predicting stock performance think little analysis formulate reasonable priors etc analyze problem second way applications like coin tossing also assign extremely small priors someone special ability actually large group could see someone could talent forcing heads really mean random experiment control known tricks still could small probability someone psychic ability rich wed 06 aug 2008 085404 0500 uai luck skill resolution