Math 160 - Cooley
Intro to Statistics
OCC
Section 4.3 – Some Rules of Probability
Probability Notation
If E is an event, then P(E) represents the probability that event E occurs. It is read “the probability of E.”
The Special Addition Rule
If event A and event B are mutually exclusive, then
P(A or B) = P(A) + P(B).
More generally, if events A, B, C, …are mutually exclusive, then
P(A or B or C or ∙ ∙ ∙ ) = P(A) + P(B) + P(C) + ∙ ∙ ∙ .
The Complementation Rule
For any event E,
P(E) = 1 – P(not E)
or
P(not E) = 1 – P(E)
The General Addition Rule
If A and B are any two events, then
P(A or B) = P(A) + P(B) – P(A and B)
 Exercises:
1)
The U.S. Coast Guard maintains a database of the number, source, and location of oil spills in U.S.
navigable and territorial waters. The following is a probability distribution for location of oil spill
events.
Location
Probability
Atlantic Ocean
0.008
Pacific Ocean
0.037
Gulf of Mexico
0.233
Great Lakes
0.020
Other Lakes
0.002
Rivers and canals
0.366
Bays and sounds
0.146
Harbors
0.161
Others
0.027
Apply the special addition rule to find the percentage of oil spills in in U.S. navigable and territorial
waters that
a)
occur in an ocean.
b)
occur in a lake or harbor.
c)
do not occur in a lake, ocean, river, or canal.
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Math 160 - Cooley
Intro to Statistics
OCC
Section 4.3 – Some Rules of Probability
 Exercises:
Experiment – Draw a card from a standard deck of cards.
2)
What is the probability that you draw a ‘6’ or a queen? ______________
3)
What is the probability that you do not draw a diamond? ______________
4)
What is the probability that you draw a ‘7’, or a ‘5’, or a ‘10’? ______________
5)
What is the probability that you do not draw an ace? ______________
6)
What is the probability that you draw a ‘5’ and clubs? ______________
7)
What is the probability that you draw an ace or spades? ______________
8)
What is the probability that you draw a face card or heart? ______________
9)
What is the probability that you draw a red card or a ‘3’? ______________
10)
What is the probability that you do not draw an even numbered card? ______________
11)
What is the probability that you draw an even number or a king? ______________
12)
Let A and B be events such that P( A)  14 , P( B)  13 , and P(A or B)  12 . Are events A and B mutually
exclusive? Determine P(A and B).
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