§ 4.3–Some Rules of Probability
Tom Lewis
Fall Term 2009
Tom Lewis ()
Outline
§ 4.3–Some Rules of Probability
1 The addition rule
2 The complement rule
3 The inclusion/exclusion principle
Fall Term 2009 1 / 6
Tom Lewis () § 4.3–Some Rules of Probability Fall Term 2009 2 / 6

The addition rule
Theorem (Additivity)
If A and B be disjoint events on a common probability space, then
P ( A ∪ B ) = P ( A ) + P ( B ) .
In general, if A
1
, A
2
, . . . , A k are disjoint events on a common probability space, then
P ( A
1
∪ A
2
∪ · · · ∪ A k
) = P ( A
1
) + P ( A
2
) + · · · + P ( A k
) .
Tom Lewis () § 4.3–Some Rules of Probability
The addition rule
Fall Term 2009 3 / 6
Problem
A bag of m& m’s contains 55 candies with the following distribution of colors:
Blue Brown Green Orange Red Yellow
11 8 8 14 8 6
An experiment consists of selecting a single candy from bag. Let Bl , Br ,
G , O, R, and Y be the events of selecting, respectively, a blue, brown, green, orange, red, or yellow candy from the bag.
Evaluate P ( Bl ) and P ( Y ) .
Evaluate the probability that the selected candy is blue or yellow.
Evaluate the probability that the selected candy is brown, green or orange.
Tom Lewis () § 4.3–Some Rules of Probability Fall Term 2009 4 / 6

The complement rule
Theorem (The complement rule)
For any event E on a probability space, P ( E ) = 1 − P ( E c
) .
Problem
Refer to the m&m data. What is the probability of not selecting an orange candy.
Tom Lewis () § 4.3–Some Rules of Probability
The inclusion/exclusion principle
Fall Term 2009 5 / 6
Theorem (Inclusion/exclusion)
If A and B are any two events on a common sample space, then
P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B )
Problem
An experiment consists of selecting a single card from a standard deck of
52 cards. What is the probability of selecting a king or a heart?
Problem
Let A and B be events on a common probability space with P ( A ) = .
3 ,
P ( B ) = .
4 and P ( A ∩ B ) = .
1 . Evaluate the following probabilities:
Find P ( A ∪ B )
Find P ( A ∩ B c
)
Tom Lewis () § 4.3–Some Rules of Probability Fall Term 2009 6 / 6