▁on ▁the ▁evidence ▁in ▁the ▁system . ▁ ▁The ▁null ▁hypothesis ▁is ▁set ▁to ▁zero ▁by ▁definition ▁( it ▁corresponds ▁to ▁“ no ▁solution ” ). ▁The ▁orthogonal ▁hypoth eses ▁“ A live ” ▁and ▁“ D ead ” ▁have ▁prob abilities ▁of ▁ 0 . 2 ▁and ▁ 0 . 5 , ▁respectively . ▁This ▁could ▁correspond ▁to ▁“ Live / D ead ▁Cat ▁Det ector ” ▁signals , ▁which ▁have ▁respective ▁reli abilities ▁of ▁ 0 . 2 ▁and ▁ 0 . 5 . ▁Finally , ▁the ▁all - en comp ass ing ▁“ E ither ” ▁hypothesis ▁( which ▁simply ▁acknowled ges ▁there ▁is ▁a ▁cat ▁in ▁the ▁box ) ▁pick s ▁up ▁the ▁s lack ▁so ▁that ▁the ▁sum ▁of ▁the ▁masses ▁is ▁ 1 . ▁The ▁belief ▁for ▁the ▁“ A live ” ▁and ▁“ D ead ” ▁hypoth eses ▁matches ▁their ▁corresponding ▁masses ▁because ▁they ▁have ▁no ▁subsets ; ▁belief ▁for ▁“ E ither ” ▁consists ▁of ▁the ▁sum ▁of ▁all ▁three ▁masses ▁( E ither , ▁A live , ▁and ▁Dead ) ▁because ▁“ A live ” ▁and ▁“ D ead ” ▁are ▁each ▁subsets ▁of ▁“ E ither ”. ▁The ▁“ A live ” ▁pla us ibility ▁is ▁ 1   −   m ▁( D ead ) ▁and ▁the ▁“ D ead ” ▁pla us ibility ▁is ▁ 1   −   m ▁( A live ). ▁ ▁In ▁other ▁way , ▁the ▁“ A live ” ▁pla us ibility ▁is ▁m ( A