Transcript Example of a Simple Event

Introductory Statistics
Lesson 3.1 A
Objective: SSBAT identify sample space and find
probability of simple events.
Standards: M11.E.3.1.1
Probability
 Measures how likely it is for something to occur
 A number between 0 and 1
 Can be written as a fraction, decimal or percent
Probability equal to 0  Impossible to happen
Probability equal to 1  Will definitely occur
Probability is used all around us and can be used to
help make decisions.
 Weather
“There is a 90% chance it will rain tomorrow.”
You can use this to decide whether to plan a trip
to the amusement park tomorrow or not.
 Surgeons
“There is a 35% chance for a successful surgery.”
They use this to decide if you should proceed with
the surgery.
Probability Experiment
 An action, or trial, through which specific results
(counts, measurements, or responses) are obtained.
Outcome
 The result of a single trial in an experiment
Example: Rolling a 2 on a die
Sample Space
 The set of ALL possible outcomes of a probability
experiment.
Example:
Experiment  Rolling a Die
Sample Space: 1, 2, 3, 4, 5, 6
Event
 A subset (part) of the sample space.
 It consists of 1 or more outcomes
 Represented by capital letters
Example:
Experiment  Rolling a Die
Event A: Rolling an Even Number
Tree Diagram
 A method to list all possible outcomes
Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
1. A probability experiment that consists of Tossing a Coin
and Rolling a six-sided die.
a) Make a tree diagram
Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
1. A probability experiment that consists of Tossing a Coin
and Rolling a six-sided die.
a) Make a tree diagram
H
1 2 3 4 5 6
Sample Space:
T
1 2 3 4 5 6
{H1, H2, H3, H4, H5, H6,T1, T2,
T3, T4, T5, T6}
Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
1. A probability experiment that consists of Tossing a Coin
and Rolling a six-sided die.
b) There are 12 outcomes
2. An experimental probability that consists of a
person’s response to the question below and that
person’s gender.
Survey Question: There should be a limit on the
number of terms a U.S. senator can serve.
Response Choices: Agree, Disagree, No Opinion
a)
Sample Space: {FA, FD, F NO, MA, MD, M NO}
b) There are 6 outcomes
3. A probability experiment that consists of tossing a
coin 3 times.
a)
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTH, TTT}
b) There are 8 outcomes
Fundamental Counting Principle
 A way to find the total number of outcomes there are
 It does not list all of the possible outcomes – it just
tells you how many there are
 If one event can occur in m ways and a second
event can occur n ways, the total number of ways
the two events can occur in sequence is m·n
 This can be extended for any number of events
In other words:
The number of ways that events can occur in sequence
is found by multiplying the number of ways each event
can occur by each other.
Take a look at a previous example and solve using the
Fundamental Counting Principle.
How many outcomes are there for Tossing a Coin and
Rolling a six sided die?
There are 2 outcomes for the coin
There are 6 outcomes for the die
 Multiply 2 times 6 together to get the total number
of outcomes
Therefore there are 12 total outcomes.
1. You are purchasing a new car. The possible
manufacturers, car sizes, and colors are listed
below. How many different ways can you select one
manufacturer, one car size, and one color?
Manufacturer: Ford, GM, Honda
Car Size: Compact, Midsize
Color: White, Red, Black, Green

3 · 2 · 4 = 24
There are 24 possible combinations.
2. The access code for a car’s security system consists
of four digits. Each digit can be 0 through 9 and the
numbers can be repeated.
 there are 10 possibilities for each digit
 10 · 10 · 10 · 10 = 10,000
There are 10,000 possible access codes.
3. The access code for a car’s security system consists
of four digits. Each digit can be 0 through 9 and the
numbers cannot be repeated.
 There are 10 possibilities for the 1st number
and then subtract 1 for the next amount and so on
 10 · 9 · 8 · 7 = 5040
There are 5,040 possible access codes.
4. How many 5 digit license plates can you make if the
first three digits are letters (which can be repeated)
and the last 2 digits are numbers from 0 to 9, which
can be repeated?
 there are 26 possible letters and 10 possible numbers

26 · 26 · 26 · 10 · 10
= 1,757,600
There are 1,757,600 possible license plates
5. How many 5 digit license plates can you make if the
first three digits are letters, which cannot be
repeated, and the last 2 digits are numbers from 0
to 9, which cannot be repeated?

26 · 25 · 24 · 10 · 9
= 1,404,000
There are 1,404,000 possible license plates
6. How many ways can 5 pictures be lined up on a wall?

5·4·3·2·1
There are 120 different ways.
Simple Event
 An event that consists of a single outcome
Example of a Simple Event
 Rolling a 5 on a die - There is only 1 outcome, {5}
Example of a Non Simple Event
 Rolling an Odd number on a die – There are 3
possible outcomes: {1, 3, 5}
Determine the number of outcomes in each event.
Then decide whether each event is simple or not?
1. Experiment: Rolling a 6 sided die
Event: Rolling a number that is at least a 4
 There are 3 outcomes (4, 5, or 6)
 Therefore it is not a simple event
Determine the number of outcomes in each event.
Then decide whether each event is simple or not?
2. Experiment: Rolling 2 dice
Event: Getting a sum of two
 There is 1 outcome (getting a 1 on each die)
 Therefore it is a simple event
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