The  probability  of  throwing  any  face  upward  will  be  6/6  =  1
in  other  words,  certainty.  Therefore,  if  the  probability  of  the
occurrence  of  an  event  be  p,  then  that  of  the  failure  of  the  event  to
occur  will  be  l—p,  provided  it  is  certain  that  the  event  must  either
occur  or  fail.
First  Principle.  The  probability  of  the  occurrence  of  an
event  is  therefore  a  proper  fraction  between  the  limits  zero  (impos-
sibility) and  unity  (certainty),  and  may  be  defined  ^as  the  ratio
between  the  number  of  ways  in  which  the  event  may  occur  and  the
number  of  ways  in  which  it  may  either  occur  or  fail.
177.  Two  Sources  of  Probability.  The  probability  of  an
event  may  be  based  upon  theory  or  experience.  The  above  case
of  throwing  a  die  is  an  example  of  the  theoretical  basis.  We  know
without  question  how  many  faces  the  die  has  and,  therefore^,  the
number  of  ways  in  which  a  certain  face  can  lie  upwards.  The
numbers  involved  are  known  absolutely.  In  the  second  case,  on
the  other  hand,  the  number  of  ways  in  which  the  event  can  occur
is  assumed  as  a  result  of  experiment  or  experience.  For  example,
if  an  event  has  occurred  a  times  and  failed  b  times  out  of  a  large
number  a-f6,  of  trials,  we  may  say  that  the  probability  of  its
occurrence,  under  the  same  conditions,  is  a/(a-\-b),  as  ])efore.
