Download PS Ch. 3.1 Notes

Sec. 3.1 – Basic Concepts of Probability and Counting
A _____________ ______________ is an action, or trial, through which specific
results are obtained.
The result of a single trial in a probability experiment is an ___________.
The set of all possible outcomes of a probability experiment is the __________
___________.
An __________ is a subset of the sample space. It may consist of one or more
outcomes.
A probability experiment consists of tossing a coin, tossing a different coin, then
tossing another different coin. Identify the sample space of the experiment.
A probability experiment consists of rolling a six-side die, then tossing a coin.
Identify the sample space of the experiment.
An event that consists of a single outcome is called a _________ _________.
Identify whether an event is a simple event from rolling a six-sided die, then
tossing a coin.
Getting a 6 on the die
Getting a 1 and then getting heads on the coin
Getting an odd number and then getting tails on the coin
Getting a head and an even prime number on the die
The Fundamental Counting Principal
If one event can occur 𝑚 ways and a second event can occur 𝑛 ways, then the
number of ways the two events can occur in sequence is 𝑚 ∙ 𝑛 ways.
Senior Banquet
Main Course
Side
Dessert
A license plate consists of 4 digits and one letter. Only odd numbers can be used
for the first digit. How many different license plates are there?
An access code has 5 digits. The first digit has to be 5 or less and cannot be 0. The
last digit cannot be 3. How many different possible access codes are there?
Types of Probability
__________ (or theoretical) probability is used when each outcome in a sample
space is equally likely to occur.
𝑃(𝐸) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑒𝑣𝑒𝑛𝑡 𝐸
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒
You roll two six-sided dice. Find the probability of each event.
Event A: Rolling a 3 on both dice.
Event B: Rolling an even number on both dice.
Event C: The sum of both numbers is seven.
Event D: Both numbers rolled are the same.
Event E: The sum of both numbers is prime.
____________ probability is based on observations obtained from probability
experiments. The empirical probability of an event E is the relative frequency of
event E.
𝑃(𝐸) =
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑒𝑣𝑒𝑛𝑡 𝐸 𝑓
=
𝑇𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑛
A company is conducting an online survey of randomly selected individuals to
determine if traffic congestion is a problem in their community. The results are
displayed in the table below.
Response
It is a serious problem.
It is a moderate problem.
It is not a problem.
Number of Times, 𝒇
123
115
82
What is the probability that a randomly selected person from the community
thinks traffic congestion is a serious problem?
What is the probability that a randomly selected person from the community
thinks traffic congestion is not a problem?
Law of Large Numbers
As an experiment is repeated over and over, the empirical probability of an event
approaches the theoretical (actual) probability of the event.
Describe how the law large numbers relates to tossing a coin 10,000 times
opposed to just 10 times.
Range of Probabilities Rule
The probability of an event E is between 0 and 1 inclusive.
0 ≤ 𝑃(𝐸) ≤ 1
The probability of a certain event is ___________.
The probability of an impossible event is ___________.
An event that occurs with a probability less than ____________ is typically
considered unusual and is highly unlikely to occur.
Complementary Events
The ________________ of event E is the set of all outcomes in a sample space
that are not included in event E. The complement of event E is denoted by
________ (“E prime”).
𝑃(𝐸) + 𝑃(𝐸 ′ ) = 1
Consider the probability experiment of rolling a six-sided die then tossing a coin.
Find the probability of the following events.
Event A: Getting a four and then tails on the coin
Event B: Not getting an even number and then getting heads
The complement of event A
The complement of event B
Answer the following questions about the frequency distribution of employee
ages at a company.
Employee Ages Frequency, 𝑓
15 to 24
54
25 to 34
366
35 to 44
233
45 to 54
180
55 to 64
125
65 and over
42
What is the probability a randomly selected employee is between 35 and 44 years
old?
What is the probability a randomly selected employee is between 25 and 54 years
old?
What is the probability a randomly selected employee is not over 54 years old?
What is the probability a randomly selected employee is not between 15 and 24
years old?