Introductory Statistics Lesson 3.1 A

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 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 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}

Examples: Find each for all of the following a) Identify the Sample Space b) Determine the number of outcomes A probability experiment that consists of Tossing a Coin and Rolling a six-sided die. b) There are 12 outcomes

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

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.

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.

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.

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.

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

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? 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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Introductory Statistics Lesson 3.1 A