introductory statistics lesson 3.1 a
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Introductory Statistics
Lesson 3.1 A
Objective: SSBAT identify sample space and find probability of simple events.
Standards: M11.E.3.1.1
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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 happenProbability equal to 1 Will definitely occur
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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.
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Probability Experiment
An action, or trial, through which specific results (counts, measurements, or responses) are obtained.
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Outcome
The result of a single trial in an experiment
Example: Rolling a 2 on a die
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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
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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
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Tree Diagram
A method to list all possible outcomes
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Examples: Find each for all of the followinga) Identify the Sample Spaceb) 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
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Examples: Find each for all of the followinga) Identify the Sample Spaceb) 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 T
1 2 3 4 5 6 1 2 3 4 5 6
Sample Space: {H1, H2, H3, H4, H5, H6,T1, T2, T3, T4, T5, T6}
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Examples: Find each for all of the followinga) Identify the Sample Spaceb) 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
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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
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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
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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
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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.
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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 coinThere are 6 outcomes for the die
Multiply 2 times 6 together to get the total number of outcomes
Therefore there are 12 total outcomes.
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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, HondaCar Size: Compact, MidsizeColor: White, Red, Black, Green
3 · 2 · 4 = 24
There are 24 possible combinations.
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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.
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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.
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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
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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
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6. How many ways can 5 pictures be lined up on a wall?
5 · 4 · 3 · 2 · 1
There are 120 different ways.
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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}
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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
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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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