▁cannot ▁be ▁tested , ▁and ▁ 2 ) ▁hypoth eses . ▁Proof ▁in ▁the ▁theory ▁of ▁probability ▁was ▁built ▁on ▁four ▁ax i oms ▁developed ▁in ▁the ▁late ▁ 1 7 th ▁century : ▁The ▁probability ▁of ▁a ▁hypothesis ▁is ▁a ▁non - negative ▁real ▁number : ▁; ▁The ▁probability ▁of ▁necessary ▁truth ▁equals ▁one : ▁; ▁If ▁two ▁hypoth eses ▁h 1 ▁and ▁h 2 ▁are ▁mut ually ▁exclusive , ▁then ▁the ▁sum ▁of ▁their ▁prob abilities ▁is ▁equal ▁to ▁the ▁probability ▁of ▁their ▁dis j unction : ▁; ▁The ▁conditional ▁probability ▁of ▁h 1 ▁given ▁h 2 ▁ ▁is ▁equal ▁to ▁the ▁un cond itional ▁probability ▁ ▁of ▁the ▁conj unction ▁h 1 ▁and ▁h 2 , ▁divided ▁by ▁the ▁un cond itional ▁probability ▁ ▁of ▁h 2 ▁where ▁that ▁probability ▁is ▁positive ▁, ▁where ▁. ▁ ▁The ▁preceding ▁ax i oms ▁provide ▁the ▁statistical ▁proof ▁and ▁basis ▁for ▁the ▁laws ▁of ▁random ness , ▁or ▁objective ▁chance ▁from ▁where ▁modern ▁statistical ▁theory ▁has ▁advanced . ▁Ex perimental ▁data , ▁however , ▁can ▁never ▁prove ▁that ▁the ▁hypoth eses ▁( h ) ▁is ▁true , ▁but ▁re lies ▁on ▁an ▁induct ive ▁inference ▁by ▁meas uring ▁the ▁probability ▁of ▁the ▁hypoth eses ▁relative ▁to ▁the ▁empir ical ▁data . ▁The ▁proof ▁is ▁in ▁the ▁rational ▁demonstr ation ▁of ▁using ▁the ▁logic ▁of ▁inference , ▁math , ▁testing , ▁and ▁ded uct ive ▁reasoning ▁of ▁significance . ▁ ▁Test ▁and ▁proof ▁▁ ▁The ▁term ▁proof ▁desc ended ▁from ▁its ▁Latin ▁roots ▁(