



Now
let's talk about using the word OR.






What
is the chance of getting a heads 


OR
a tails when you flip a coin? 





Well
hey, 


the
coin is either going to come up heads 


or
it is going to come up tails. 


That
means there is a 100% chance 


of
getting a heads or a tails. 





100%
= 1






The
chance of getting a heads is ... 











The
chance of getting a tails is ... 











It
looks like we have a pattern here too! 


It
looks like when we have the word OR 


with
independent events, we just add up the fractions. 


Like
this ... 





The
chance of a coin flip coming up heads OR tails is ... 











That
does work ... sometimes. 


But
sometimes it doesn't work.



Watch
... 





What
is the chance of getting a heads on the first flip of a coin 


OR
a heads on the second flip of the coin? 





If
we use the "just add them up" plan, we get ...






The
chance of getting a heads on the first flip 


or
the second flip is ... 











A
100% chance means that he thing will absolutely happen.



But
hey, both flips COULD come up tails. 


So
the chance that either the first flip will be heads 


OR
the second flip will be heads CAN'T be 100%. 





So
what's the deal? Why didn't this one work? 





It
doesn't work because the two things can overlap. 


That
is, both flips could be heads.



We
could draw a picture of this ... 











So
now we have to decide just exactly what we mean 


when
we say OR.



Do
we mean: 


One
thing happens or the other thing happens or both. 


Or
do we mean: 


One
thing happens or the other thing happens but not both. 





Long
ago, somebody decided that what OR means is ... 


"One
thing happens or the other thing happens OR
BOTH." 





If
they wanted to leave out the "or both" part, they call it
an ... 





EXCLUSIVE
OR






That
name is pretty long, 


so
sometimes they shorten it to ... 





XOR






Review
Time: 






AND 
One AND the
other. 




OR 
One OR the
other OR both 




XOR 
One or the
other BUT NOT BOTH 






When
we figure out the ones that use OR, 


we
need a way not to count the overlap part twice. 











If
you look close, you will see that the overlap part 


is
where the first flip comes up heads 


and
the second flip comes up heads too. 





To
get rid of the double counting. 


That
means the chance of one thing OR the other 


(or
both) happening, is ... 











So
for our coin flips, we have ... 

















So
there is a 75% chance that the first flip, 


or
the second flip, or both, will be a heads. 





There is
another way to look at this OR calculation 


that
might be easier to understand. 


If it is,
great. If not, forget it. At least for now. 


Here it
is ... 





Think
about what you don't want to happen. 


You are
looking for the chance of a heads 


on
the first flip OR the second
flip. 


The
only way you don't get that is if you get a tails 


on
the first flip AND the second
flip 


Rather
than calculating the OR with all it's overlaps to worry about, 


just
calculate the other side, THE AND, and subtract that from
100%. 





An
AND is just a multiplication. 





Example: 





What's
the chance of getting a heads on the first or second coin flip. 


The
opposite of this is getting a tails on the first AND second
flip, 


so
calculate that and subtract it from 100%. 





The
chance of getting a tails on the first flip is 50% ... 


The
chance of getting a tails on the second flip is 50% ... 





The
chance of getting a tails on the first AND second flips is ... 





50% × 50%
= 25%






So
the chance of this NOT happening, is ... 





100%  25%
= 75%






And
if we didn't get a tails on the first and second flips, 


that
means one or the other or both was a heads. 


The
same answer, what a shock! 





copyright 2005 Bruce Kirkpatrick 
