We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byGunnar Paull
Modified over 2 years ago
AP Statistics Section 6.2C Independent Events & The Multiplication Rule
Consider a standard deck of 52 playing cards. If one card is chosen at random, what is the probability the card is red?
If the first card is red and a second card is chosen at random from the same deck, the probability that this card is also red will depend upon what was done with the first card.
If the first card was returned to the deck, the probability the second card is red will be…
If the first card was not returned to the deck, the probability the second card is red will be…
In the first case, knowing that the first card pulled from the deck was red did not affect the probability that the second card was red.
This is not true, however, in the second case.
In the second case, knowing that the first card pulled from the deck was red affected the probability that the second card was red.
Two events are independent if knowing that the one occurs does not affect the probability that the other one occurs.
Example: Determine if the two events A and B are independent. independent
Example: Determine if the two events A and B are independent. dependent
Example: Determine if the two events A and B are independent. dependent
Example: Are an event A and A c independent? Why are why not? Note: Disjoint events are not independent.
Disjoint and independent do not mean the same thing.
Consider rolling a 6-sided die and then flipping a coin. What is the probability of rolling a 3 and getting a heads on the coin?
Example: Find the following probabilities. a. selecting 4 cards with replacement from a standard deck and having all 4 be clubs
Example: Find the following probabilities. b. rolling five 6-sided dice and getting five twos
Example: Find the following probabilities. c. selecting 4 cards with replacement from a standard deck and getting at least one club
Example: Find the following probabilities. d. rolling five 6-sided dice and getting at least one two
Multiplication Rule Statistics B Mr. Evans. Addition vs. Multiplication Rule The addition rule helped us solve problems when we performed one task and.
Conditional Probability and the Multiplication Rule NOTES Coach Bridges.
Independent and Dependent Events Lesson 6.6. Getting Started… You roll one die and then flip one coin. What is the probability of : P(3, tails) = 2. P(less.
Beginning Probability Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial Probability Empirical vs Theoretical.
Probability. Probability of an Event A measure of the likelihood that an event will occur. Example: What is the probability of selecting a heart from.
Section 5.3 Independence and the Multiplication Rule.
Conditional Probability 423/what-is-your-favorite-data-analysis-cartoon 1.
PROBABILITY 4 corners review. A.One outcome or a collection of outcomes B. Based on relative frequency- what actually occurs during an experiment C. When.
AP Statistics Section 6.2 A Probability Models. If you tossed a coin 5 times, would you be surprised if you got heads exactly 1 time? If you tossed a.
Probability of 2 Independent Events Example – Two Independent Events.
7/20 The following table shows the number of people that like a particular fast food restaurant. 1)What is the probability that a person likes Wendys?
Probability Predictions Ch. 1, Act. 5. Probability The study of random events. Random events are things that happen without predictability – e.g. the.
AP STATISTICS Section 6.2 Probability Models. Objective: To be able to understand and apply the rules for probability. Random: refers to the type of order.
Chapter 1:Independent and Dependent Events. What is dependent? Any real-life examples? Any math examples? What is independent? Any real-life.
Discrete Math Section 16.1 Find the sample space and probability of multiple events The probability of an event is determined empirically if it is based.
Academy Algebra II/Trig 14.3: Probability HW: worksheet Test: Thursday, 11/14.
7/20 The following table shows the number of people that like a particular fast food restaurant. 1)What is the probability that a person likes Wendy’s?
Recap from last lesson Compliment Addition rule for probabilities Mutually exclusive events Exhaustive events this is defined as it is certain at least.
1 Probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing, and.
PROBABILITY: Combining Two Events Jonathan Fei. Definitions RANDOM EXPERIMENT: any procedure or situation that produces a definite outcome that may not.
Independent and Dependent Events. Learning Targets Determine when events are dependent or independent. Learn to use the multiplication rule of probability.
Section 2 Probability Rules – Compound Events Compound Event – an event that is expressed in terms of, or as a combination of, other events Events A.
Probability Assessment Created by: Megan Seeman August 2, 2011.
CONDITIONAL PROBABILITY 3.2 Raise your hand when you are finished reading.
Dependent and Independent Events. Events are said to be independent if the occurrence of one event has no effect on the occurrence of another. For example,
DEFINITION INDEPENDENT EVENTS: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.
Chapter 12 – Probability and Statistics 12.4 – Multiplying Probabilities.
What is the probability of two or more independent events occurring? I NDEPENDENT EVENTS are events that are distinct and separate. – Each event does.
1.4 Equally Likely Outcomes. The outcomes of a sample space are called equally likely if all of them have the same chance of occurrence. It is very difficult.
Describing Probability Outcomes, Sample Spaces and Probability Models.
What are the chances of that happening?. What is probability? The mathematical expression of the chances that a particular event or outcome will happen.
7/ people were surveyed for their favorite fast-food restaurant. 1. What is the probability that a person likes Wendy’s? 2. What is the probability.
Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring.
5.3 Independence and the Multiplication Rule. ● The Addition Rule shows how to compute “or” probabilities P(E or F) under certain conditions ● The Multiplication.
CONDITIONAL PROBABILITY and INDEPENDENCE In many experiments we have partial information about the outcome, when we use this info the sample space becomes.
Chapter 12 Sec 4 Multiplying Probability. 2 of 13 Algebra 2 Chapter 12 Sections 4 & 5 Independent Events In situations with two independent events, you.
You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.
Refreshing Your Skills for Chapter 10. If you flip a coin, the probability that it lands with heads up is 1/2. If you roll a standard die, the probability.
Section 5.2 Some Probability Rules Compound Events 5.2 / 1.
Section Probability Models AP Statistics toddfadoir.com/apstats.
Sec 4.4 The multiplication Rule and conditional probability.
PROBABILITY How to win at Monopoly. Flipping a Coin Will a flipped coin be HEADS or TAILS? Can’t know for sure! Is one more LIKELY?
Each time an experiment such as one toss of a coin, one roll of a dice, one spin on a spinner etc. is performed, the result is called an ___________.
D4/2 Use the following Venn diagram to answer the question: If the 2 ovals in the Venn diagram above represent events A and B, respectively, what is ?
Probability of Compound Events compound event combines two or more events, using the word and or the word or. The word “or” in probability means Union.
Section Probability Models AP Statistics December 2, 2010.
Probability theory and average-case complexity. Review of probability theory.
P4. Probability Essential Question: How is an independent event defined?
© 2016 SlidePlayer.com Inc. All rights reserved.