



When
people try to tell how likely it is that something will happen,



they
often use percents. 





Like when
TV weather types try to predict if it will rain tomorrow. 





A 100
percent chance of rain tomorrow means that it WILL rain tomorrow. 





A zero
percent chance of rain tomorrow means that it WILL NOT rain
tomorrow. 





A fifty
percent chance of rain tomorrow means 


that
there is an equal chance that it WILL or WILL NOT rain tomorrow. 





Some
people call an equal chance between two things a coin toss. 





Take a
coin. Flip it end over end in the air. 


If the
coin and the flip are fair, 


there is
an equal chance that either side will end up on top. 





Once
again, there is an equal chance that either side 


will end
up on top any time the coin is flipped. 





No matter
what happened on the last flip or the last hundred flips, 


each flip
is a whole new ballgame. 





Examples: 


1) A
penny comes up heads the last ten times that you flipped it. 





What is
the chance that it will come up heads on the next flip? 





FIFTY
PERCENT






2) The
same penny has come up tails the last ten times that you have
flipped it. 





What is
the chance that it will come up heads this time? 





FIFTY
PERCENT






3) The
last six flips of the penny have come up 


HEADS 
TAILS  HEADS  TAILS  HEADS  TAILS. 


What is
the chance that it will come up heads on the next flip? 





FIFTY
PERCENT






So great.
Any time that you flip a coin it has an equal chance 


of coming
up heads or coming up tails. 


It
doesn't make any difference what happened 


on any
flip that came before the current one. 


The
chance of the coin coming up heads on any flip is 





FIFTY
PERCENT






Because
each flip stands on it's own 


and does
not depend on what happened before, 


statistics
types call coin flips 





INDEPENDENT
EVENTS






Lot's of
things that happen over and over are independent events. 





Rolls
of a pair of dice are independent events. 





What
number comes up on a roulette wheel each time is an independent
event. 





If the
situation is the same after the event as it was before the event, 


the
events are probably independent. 





There
are also lots of events that are NOT independent. 





They
do depend on what has happened before. 


If
it is 100 degrees outside today, it is not likely it will snow here
tomorrow. 


If
the first card you are dealt from a regular deck is the king of
hearts, 


it's
not very likely the second will be the king of hearts too. 





We
call these dependent events. 





copyright 2005 Bruce Kirkpatrick 
