Probability and Simulation Rules in Probability. Probability Rules 1. Any probability is a number between 0 and 1 0 ≤ P[A] ≤ 1 0 ≤ P[A] ≤ 1 2. The sum.

Slides:

Advertisements

Similar presentations

A.P. STATISTICS LESSON 6 – 2 (DAY2) PROBABILITY RULES.

Advertisements

Section 5.1 and 5.2 Probability

Probability Sample Space Diagrams.

Chapter 5: Probability: What are the Chances?

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 5: Probability: What are the Chances? Section 5.2 Probability Rules.

PROBABILITY IDEAS Random Experiment – know all possible outcomes, BUT

Probability Rules l Rule 1. The probability of any event (A) is a number between zero and one. 0 < P(A) < 1.

5.2A Probability Rules! AP Statistics.

Section 5.2 The Addition Rule and Complements

AP Statistics Notes Chapter 14 and 15.

11/20/ Probability Rules.

AP Statistics Chapter 6 Notes. Probability Terms Random: Individual outcomes are uncertain, but there is a predictable distribution of outcomes in the.

Special Topics. General Addition Rule Last time, we learned the Addition Rule for Mutually Exclusive events (Disjoint Events). This was: P(A or B) = P(A)

The Practice of Statistics

Tree Diagram Worksheet

Basic Probability Rules Let’s Keep it Simple. A Probability Event An event is one possible outcome or a set of outcomes of a random phenomenon. For example,

Probability Probability is the measure of how likely an event is. An event is one or more outcomes of an experiment. An outcome is the result of a single.

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 5: Probability: What are the Chances? Section 5.2 Probability Rules.

Probability Models.  Understand the term “random”  Implement different probability models  Use the rules of probability in calculations.

5.1 Randomness  The Language of Probability  Thinking about Randomness  The Uses of Probability 1.

Chapter 6 Review Fr Chris Thiel 13 Dec 2004 What is true about probability? The probability of any event must be a number between 0 and 1 inclusive The.

Probability. Rules  0 ≤ P(A) ≤ 1 for any event A.  P(S) = 1  Complement: P(A c ) = 1 – P(A)  Addition: If A and B are disjoint events, P(A or B) =

Probability Basics Section Starter Roll two dice and record the sum shown. Repeat until you have done 20 rolls. Write a list of all the possible.

Sixth lecture Concepts of Probabilities. Random Experiment Can be repeated (theoretically) an infinite number of times Has a well-defined set of possible.

Chapter 6 Day 2. Multiplication Principle – if you do one task a number of ways and a second task b number of ways, then both tasks can be done a x b.

Stat 1510: General Rules of Probability. Agenda 2  Independence and the Multiplication Rule  The General Addition Rule  Conditional Probability  The.

+ Unit 5: Probability: What are the Chances? Lesson 2 Probability Rules.

Chapter 10 – Data Analysis and Probability 10.7 – Probability of Compound Events.

AP Statistics Section 6.2 B Probability Rules. If A represents some event, then the probability of event A happening can be represented as _____.

AP Statistics Probability Rules. Definitions Probability of an Outcome: A number that represents the likelihood of the occurrence of an outcome. Probability.

AP Statistics Chapter 6 Section 3. Review of Probability Rules 1.0 < P(A) < 1 2.P(S) = 1 3.Complement Rule: For any event A, 4.Addition Rule: If A and.

Probability Probability Day 3 Introduction to Probability Probability of Independent Events.

+ Section 5.2 Probability Rules After this section, you should be able to… DESCRIBE chance behavior with a probability model DEFINE and APPLY basic rules.

6.2 – Probability Models It is often important and necessary to provide a mathematical description or model for randomness.

Probability Models Section 6.2. The Language of Probability What is random? What is random? Empirical means that it is based on observation rather than.

Probability What is the probability of rolling “snake eyes” in one roll? What is the probability of rolling “yahtzee” in one roll?

Section Probability Models AP Statistics December 2, 2010.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 5 Probability: What Are the Chances? 5.2.

Conditional Probability 423/what-is-your-favorite-data-analysis-cartoon 1.

Probability Models Section 6.2.

Section 5.1 and 5.2 Probability

Adding Probabilities 12-5

CHAPTER 5 Probability: What Are the Chances?

Chapter 5: Probability: What are the Chances?

Chapter 6 6.1/6.2 Probability Probability is the branch of mathematics that describes the pattern of chance outcomes.

PROBABILITY AND PROBABILITY RULES

Probability Rules!!! … and yea… Rules About Probability

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Probability Models Section 6.2.

Section 6.2 Probability Models

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Mr. Reider AP Stat November 18, 2010

Chapter 5: Probability: What are the Chances?

Section Probability Models

Chapter 5: Probability: What are the Chances?

Probability Rules Rule 1.

Chapter 5: Probability: What are the Chances?

Chapter 6: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

Chapter 5: Probability: What are the Chances?

6.2 Probability Models.

Chapter 5: Probability: What are the Chances?

Unit 6: Probability: What are the Chances?

A random experiment gives rise to possible outcomes, but any particular outcome is uncertain – “random”. For example, tossing a coin… we know H or T will.

Presentation transcript:

Probability and Simulation Rules in Probability

Probability Rules 1. Any probability is a number between 0 and 1 0 ≤ P[A] ≤ 1 0 ≤ P[A] ≤ 1 2. The sum of all the probabilities of all possible outcomes must equal 1. P[S] = 1 P[S] = 1 3. If two events have no outcomes in common, the probability that the one or the other occurs is the sum of their individual probabilities. P[A or B] = P[A] + P[B] P[A or B] = P[A] + P[B] 4. The probability that an event does not occur is 1 minus the probability that the event does occur. P[A’] = 1 - P(A) P[A’] = 1 - P(A)

Probability Rules (Examples) 1. 0 ≤ P[A] ≤ 1: any proportion is always between 0 and 1 2. P[S] = 1 : probability of getting 1, 2, 3, 4, 5, or 6 in tossing a die is ⅙ + ⅙ + ⅙ + ⅙ + ⅙ + ⅙ = 6/6 or 1 3. P[A or B] = P[A] + P[B]: tossing a coin 3 times A: getting all tails B: getting all heads P[A or B] = ⅛ + ⅛ = 2/4 or ¼ 4. P[A’] = 1 - P(A): Probability of getting A in AP Stat is 20% therefore, the probability of NOT getting an A in AP Stats is 80%

Draw a woman aged years old at random and record her marital status. If we drew many women, this is the proportion we would get. Here’s the probability model: Marital Status Never Married MarriedWidowedDivorced Probability P(not married) = 1-P(married) = = Therefore there are 37.8% of women that are NOT married

Marital Status Never Married MarriedWidowedDivorced Probability P(never married or divorced) = P(never married) + P(divorced) = = Therefore there are 37.3% of women in this group that are either never married or divorced

Venn Diagram S A BA’ A Disjoint events A and B (mutually exclusive events) A’ = complement of A

P[A or B ] = P[A] + P[B]P[A and B ] = P[A] x P[B] Addition Rule of union event Multiplication Rule of Independent Variables Ex: Probability of getting a sum of 3 and probability of getting a sum of 5 when you roll a pair of dice Ex: Probability of getting getting a 4 and then another 4 when you roll a die twice P[A or B] = 2/36 + 4/36 = 6/36 = 17% P[A and B] = 1/6 x 1/6 = 1/36 = 2.8% P [A ∩ B] P [A ∪ B]