The Addition Rule
Mutually Exclusive Events
 Two events A and B are mutually exclusive if A
and B cannot occur at the same time.
EX: Decide if the events are
mutually exclusive:
EVENT A
Randomly selecting a 20
year old student
Randomly selecting a
vehicle that is a Ford
EVENT B
Randomly selecting a
student with blue eyes
Randomly selecting a
vehicle that is a Toyota
Randomly selecting a JACK Randomly selecting a FACE
from a deck of cards
card from a deck of cards
The Addition Rule
 The Probability that Event A OR Event B will
occur is:
 P(A or B) = P(A) + P(B) – P(A and B)
 If A and B are mutually exclusive, then:
 P(A or B) = P(A) + P(B)
EX: Find each Probability
14. A math conference has an attendance of 4950
people. Of these, 2110 are college profs and
2575 are female. Of the college profs, 960 are
female.
a) Are the events “selecting a female” and
“selecting a college prof” mutually exclusive?
b) The conference selects people at random
to win prizes. Find the probability that a
selected person is a female or a college prof.
18. You roll a die. Find each Probability
a) Rolling a 5 or a number greater than 3.
b) Rolling a number less than 4 or an even
number.
c) Rolling a 2 or an odd number.
Additional Topics in Probability &
Counting
Permutation:
… an ordered arrangement of objects.
The number of different permutations of n
distinct objects is n!
n! = n(n – 1)(n – 2)(n – 3)….(3)(2)(1)
NOTE: 0! = 1
Permutations of n objects
taken r at a time…
 Notation: nPr
 nPr =
n!
(n – r)!
 ORDER MATTERS!!!
EXAMPLES
 20. Eight people compete in a downhill ski
race. Assuming that there are no ties, in how
many different orders can the skiers finish?
 A psychologist shows a list of eight activities to
her subject. How many ways can the subject
pick a first, second, and third activity?
Distinguishable Permutations
 The number of distinguishable permutations of n
objects, where n1 are of 1 type, n2 are of another
type, and so on… is:

n!
(n1!) (n2!) (n3!) .. (nk!)
EX
 How many distinguishable permutations are
there using the letters in the word ALPHA?
 In the word COMMITTEE?
Combinations
A selection of r objects from a group of n objects
is denoted nCr
 n Cr =
n!
(n – r)!r!
ORDER DOES NOT MATTER!!!
EX
 A three person committee is to be appointed from
a group of 15 employees. In how many ways can
this committee be formed?
 If 6 of the 15 employees are women, what is the
probability that a randomly chosen 3-person
committee is all women?