
There are 10 chips in a bag, numbered from 1 to 10.
Draw a numbered chip
from the bag:
The sample space is:

What is the probability
of drawing the chip
numbered 7?
The probability will
be "one out of 10"
or

What is the probability
of drawing any chip
number that is not
numbered 7?
The probability will
be "nine out of 10"
or

If we combine (add) the probability of drawing a 7 with the probability of not drawing a 7,
we get the probability of drawing all of the chips, 100%, or 1.
When asked to find the probability that an event did NOT occur,
the answer will be 1 minus the probability that the event did occur. 
The probability of not drawing the 7,
is the probability of what is "left in the sample space", or

Since the sum of probabilities of all possible events in a sample space equals 1,
the probability that
event A will not occurs is equal to 1 minus the probability that event A will occur.


In future courses, you will see that this situation of dealing with "NOT"
is defined as being a "complement".
"The complement of event A is everything else in the sample space that is NOT in event A."
A die is rolled. What is the probability of not rolling a 6? 
P(6) = 1/6
P(not 6) = 1  1/6 = 5/6 
A spinner is divided into 4 sections of equal size.
What is the probability of not spinning a 2? 

P(spinning 2) = 1/4
P(not spinning 2) = 1  1/4 = 3/4 
A gum ball machine contains gum balls of five different colors:
36 red, 44 white, 15 blue, 20 green, and 5 orange.
There are 120 gum balls in total in the machine.
The machine dispenser randomly selects one gum ball.
What is the probability that the gum ball selected is:


a.) green? a.) probability of green is 20/120 = 1/6.
b.) not green? b.) probability of not green is 1  1/6 = 5/6.
c.) not orange? c.) probability of not orange is 1  P(orange) = 1  5/120 = 1  1/24 = 23/24.
d.) orange? d.) probability of orange is 1/24.
e.) red, white, or blue?
e.) probability of red, white or blue is 36/120 + 44/120 + 15/120 = 95/120 = 19/24.
f.) not a color in the flag of the USA?
f.) use the "complement" of the answer to part e. 1  19/24 = 5/24.

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