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

A method to list all possible outcomes . Teacher 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

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. 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. . Teacher 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 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.

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 can be repeated.  there are 10 possibilities for each digit  10 · 10 · 10 · 10 = 10,000 There are 10,000 possible access codes.

There are 5,040 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 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}

Experiment: Rolling a 6 sided die 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

2. Experiment: Rolling 2 dice Event: Getting a sum of two 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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