Ex
There are 15 dogs entered in a show.
How many ways can first,
second, and third place be awarded?
N=15
R=3
15
P
3
15!/(133)!= 3,730 ways
•
Combination of
n
objects taken
r
at a time 
A selection of
r
objects from a group of
n
objects without regard to order
n
C
r
Ex
There are 13 students in a club.
How many ways can four
students be selected to attend a conference?
N=13
R=4
13
C
4
13!/(134)!(4!)= 715 ways
Classical (theoretical) Probability 
Each outcome in a sample
space is equally likely
Empirical (statistical) Probability 
Based on observations obtained
from probability experiments. The relative frequency of an event.
4!
(4*3*2*1)=24
How many 4 letter TV call signs are possible, if each sign must start
with either a K or W?
1
st
letter=2 (K or W)
2
nd
letter=26
3
rd
letter=26
4
th
letter=26
2*26*26*26=35,152 possibilities.
Chapter 3 Review problems
Ex
On the basis of prior counts, a quality control officer says there is
a 0.05 probability that a randomly chosen part is defective.
Empirical probability
Ex
The probability of randomly selecting five cards of the same suit
(a flush) from a standard deck is about 0.0005.
Classical
Ex
The chance that corp A’s stock price will fall today is 75%.
Subjective Probability
Ex
The probability of rolling 2 sixsided dice and getting a sum
greater than nine is 1/6.
Classical probability
#of employees
04
59
1019
2099
100
+
Percent of
firms
60.8%
17.7
%
10.8
%
8.9%
1.8
%
Ex
What is the probability that a randomly selected firm will have at
least 10 employees?
P
(at least 10) =0.108+0.089+0.018= 0.215
Ex
What is the probability that a randomly selected firm will have
fewer than 20 employees?
P
(less than 20)= .608+.177+.108= .893
Ex
Tossing a coin four times, getting four heads, and tossing it a fifth
time and getting a head.
Independent.
The first event doesn’t
affect the outcome of the second event.
Ex
Taking a driver’s education course and passing the drivers license
exam.
Dependant.
You have to take the course to pass the exam.
Ex
You are shopping, and your roommate has asked you to pick up
toothpaste and dental rinse.
However, your roommate did not tell
you which brands to get.
The store has 8 brands of toothpaste and 5
brands of dental rinse.
What is the probability that you will purchase
the correct brands of both products
?
P
(correct toothpaste and
dental rinse) =
P
(correct toothpaste) *
P
(correct dental rinse)
=(1/8)*(1/5)= 0.025
Ex
Event A: Randomly selecting a red jelly bean from a jar.
Event B: Randomly selecting a yellow jelly bean from the same jar.
Mutually exclusive because both events cannot occur at the same
time.
Ex
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 Fall '10
 Raney
 Normal Distribution, ex, Ex A literacy magazine

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